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Characterizing NIP henselian fields J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-03-08 Sylvy Anscombe, Franziska Jahnke
In this paper, we characterize NIP (Not the Independence Property) henselian valued fields modulo the theory of their residue field, both in an algebraic and in a model-theoretic way. Assuming the conjecture that every infinite NIP field is either separably closed, real closed, or admits a nontrivial henselian valuation, this allows us to obtain a characterization of all theories of NIP fields.
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Multigraded algebras and multigraded linear series J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-03-07 Yairon Cid-Ruiz, Fatemeh Mohammadi, Leonid Monin
This paper is devoted to the study of multigraded algebras and multigraded linear series. For an Ns$\mathbb {N}^s$-graded algebra A$A$, we define and study its volume function FA:N+s→R$F_A:\mathbb {N}_+^s\rightarrow \mathbb {R}$, which computes the asymptotics of the Hilbert function of A$A$. We relate the volume function FA$F_A$ to the volume of the fibers of the global Newton–Okounkov body Δ(A)$\Delta
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Reversible primes J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-03-07 Cécile Dartyge, Bruno Martin, Joël Rivat, Igor E. Shparlinski, Cathy Swaenepoel
For an n$n$-bit positive integer a$a$ written in binary as a=∑j=0n−1εj(a)2j,$ {a} = \sum _{j=0}^{n-1} \varepsilon _{j}(a) \,2^j,$ where εj(a)∈{0,1}$\varepsilon _j(a) \in \lbrace 0,1\rbrace$, j∈{0,…,n−1}$j\in \lbrace 0, \ldots , n-1\rbrace$, εn−1(a)=1$\varepsilon _{n-1}(a)=1$, let us define a←=∑j=0n−1εj(a)2n−1−j,$ \overleftarrow{a} = \sum _{j=0}^{n-1} \varepsilon _j(a)\,2^{n-1-j},$ the digital
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Holomorphicity of totally geodesic Kobayashi isometry between bounded symmetric domains J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-03-08 Sung-Yeon Kim, Aeryeong Seo
In this paper, we study the holomorphicity of totally geodesic Kobayashi isometric embeddings between bounded symmetric domains. First, we show that for a C1$C^1$-smooth totally geodesic Kobayashi isometric embedding f:Ω→Ω′$f\colon \Omega \rightarrow \Omega ^{\prime }$ where Ω$\Omega$, Ω′$\Omega ^{\prime }$ are bounded symmetric domains, if Ω$\Omega$ is irreducible and rank(Ω)⩾rank(Ω′)$\text{rank}(\Omega)
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Incommensurable lattices in Baumslag–Solitar complexes J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-03-08 Max Forester
This paper concerns locally finite 2-complexes Xm,n$X_{m,n}$ that are combinatorial models for the Baumslag–Solitar groups BS(m,n)$BS(m,n)$. We show that, in many cases, the locally compact group Aut(Xm,n)$\operatorname{Aut}(X_{m,n})$ contains incommensurable uniform lattices. The lattices we construct also admit isomorphic Cayley graphs and are finitely presented, torsion-free, and coherent.
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An interpolation inequality involving LlogL spaces and application to the characterization of blow-up behavior in a two-dimensional Keller–Segel–Navier–Stokes system J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-03-10 Yulan Wang, Michael Winkler
In a smoothly bounded two-dimensional domain Ω$\Omega$ and for a given nondecreasing positive unbounded ℓ∈C0([0,∞))$\ell \in C^0([0,\infty))$, for each K>0$K>0$ and η>0$\eta >0$ the inequality
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A characterization for the defect of rank one valued field extensions J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-03-05 Josnei Novacoski
In this paper, we present a characterization for the defect of a simple algebraic extension of rank one valued fields using the key polynomials that define the valuation. As a particular example, this gives the classification of defect extensions of degree p$p$ as dependent or independent presented by Kuhlmann.
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Rubber tori in the boundary of expanded stable maps J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-22 Francesca Carocci, Navid Nabijou
We investigate torus actions on logarithmic expansions in the context of enumerative geometry. Our main result is an intrinsic and coordinate-free description of the higher rank rubber torus appearing in the boundary of the space of expanded stable maps. The rubber torus is constructed canonically from the tropical moduli space, and its action on each stratum of the expanded target is encoded in a
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Demushkin groups of uncountable rank J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-18 Tamar Bar-On, Nikolay Nikolov
We extend the theory of countably generated Demushkin groups to Demushkin groups of arbitrary rank. We investigate their algebraic properties and invariants, count their isomorphism classes, and study their realization as absolute Galois group. At the end, we compute their profinite completion and conclude with some results on profinite completion of absolute Galois groups.
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Categorical Torelli theorems for Gushel–Mukai threefolds J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-22 Augustinas Jacovskis, Xun Lin, Zhiyu Liu, Shizhuo Zhang
We show that a general ordinary Gushel–Mukai (GM) threefold X$X$ can be reconstructed from its Kuznetsov component Ku(X)$\mathcal {K}u(X)$ together with an extra piece of data coming from tautological subbundle of the Grassmannian Gr(2,5)$\mathrm{Gr}(2,5)$. We also prove that Ku(X)$\mathcal {K}u(X)$ determines the birational isomorphism class of X$X$, while Ku(X′)$\mathcal {K}u(X^{\prime })$
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Exceptional biases in counting primes over function fields J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-21 Alexandre Bailleul, Lucile Devin, Daniel Keliher, Wanlin Li
We study how often exceptional configurations of irreducible polynomials over finite fields occur in the context of prime number races and Chebyshev's bias. In particular, we show that three types of biases, which we call “complete bias,” “lower order bias,” and “reversed bias,” occur with probability going to zero among the family of all squarefree monic polynomials of a given degree in Fq[x]${\mathbb
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Volume of Seifert representations for graph manifolds and their finite covers J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-21 Pierre Derbez, Yi Liu, Shicheng Wang
For any closed orientable 3-manifold, there is a volume function defined on the space of all Seifert representations of the fundamental group. The maximum absolute value of this function agrees with the Seifert volume of the manifold due to Brooks and Goldman. For any Seifert representation of a graph manifold, the authors establish an effective formula for computing its volume, and obtain restrictions
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One-sided sharp thresholds for homology of random flag complexes J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-14 Andrew Newman
We prove that the random flag complex has a probability regime where the probability of nonvanishing homology is asymptotically bounded away from zero and away from one. Related to this main result, we also establish new bounds on a sharp threshold for the fundamental group of a random flag complex to be a free group. In doing so, we show that there is an intermediate probability regime in which the
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Discrete logarithmic Sobolev inequalities in Banach spaces J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-12 Dario Cordero-Erausquin, Alexandros Eskenazis
Let Cn={−1,1}n$\mathcal {C}_n=\lbrace -1,1\rbrace ^n$ be the discrete hypercube equipped with the uniform probability measure σn$\sigma _n$. We prove that if (E,∥·∥E)$(E,\Vert \cdot \Vert _E)$ is a Banach space of finite cotype and p∈[1,∞)$p\in [1,\infty)$, then every function f:Cn→E$f:\mathcal {C}_n\rightarrow E$ satisfies the dimension-free vector-valued Lp$L_p$ logarithmic Sobolev inequality
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Multilinear rough singular integral operators J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-07 Loukas Grafakos, Danqing He, Petr Honzík, Bae Jun Park
We study m$m$-linear homogeneous rough singular integral operators LΩ$\mathcal {L}_{\Omega }$ associated with integrable functions Ω$\Omega$ on Smn−1$\mathbb {S}^{mn-1}$ with mean value zero. We prove boundedness for LΩ$\mathcal {L}_{\Omega }$ from Lp1×⋯×Lpm$L^{p_1}\times \cdots \times L^{p_m}$ to Lp$L^p$ when 1
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Algebraically generated groups and their Lie algebras J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-07 Hanspeter Kraft, Mikhail Zaidenberg
The automorphism group Aut(X)$\operatorname{Aut}(X)$ of an affine variety X$X$ is an ind-group. Its Lie algebra is canonically embedded into the Lie algebra Vec(X)$\operatorname{Vec}(X)$ of vector fields on X$X$. We study the relations between subgroups of Aut(X)$\operatorname{Aut}(X)$ and Lie subalgebras of Vec(X)$\operatorname{Vec}(X)$. We show that a subgroup G⊆Aut(X)$G\subseteq \operatorname{Aut}(X)$
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Decomposition numbers for abelian defect RoCK blocks of double covers of symmetric groups J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-31 Matthew Fayers, Alexander Kleshchev, Lucia Morotti
We calculate the (super)decomposition matrix for a RoCK block of a double cover of the symmetric group with abelian defect, verifying a conjecture of the first author. To do this, we exploit a theorem of the second author and Livesey that a RoCK block B ρ , d $\mathcal {B}^{\rho,d}$ is Morita superequivalent to a wreath superproduct of a certain quiver (super)algebra with the symmetric group S d $\mathfrak
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Universally defining Z in Q with 10 quantifiers J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-31 Nicolas Daans
We show that for a global field K $K$ , every ring of S $S$ -integers has a universal first-order definition in K $K$ with 10 quantifiers. We also give a proof that every finite intersection of valuation rings of K $K$ has an existential first-order definition in K $K$ with 3 quantifiers.
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Determining a nonlinear hyperbolic system with unknown sources and nonlinearity J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-31 Yi-Hsuan Lin, Hongyu Liu, Xu Liu
This paper is devoted to some inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. It is shown in several generic scenarios that one can uniquely determine the nonlinearity and/or the sources by using passive or active boundary observations. In order to exploit
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Gröbner bases, symmetric matrices, and type C Kazhdan–Lusztig varieties J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-01 Laura Escobar, Alex Fink, Jenna Rajchgot, Alexander Woo
We study a class of combinatorially defined polynomial ideals that are generated by minors of a generic symmetric matrix. Included within this class are the symmetric determinantal ideals, the symmetric ladder determinantal ideals, and the symmetric Schubert determinantal ideals of A. Fink, J. Rajchgot, and S. Sullivant. Each ideal in our class is a type C analog of a Kazhdan–Lusztig ideal of A. Woo
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Lie theory and cohomology of relative Rota–Baxter operators J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-02-01 Jun Jiang, Yunhe Sheng, Chenchang Zhu
In this paper, we establish a local Lie theory for relative Rota–Baxter operators of weight 1. First we recall the category of relative Rota–Baxter operators of weight 1 on Lie algebras and construct a cohomology theory for them. We use the second cohomology group to study infinitesimal deformations of relative Rota–Baxter operators and modified r $r$ -matrices. Then we introduce a cohomology theory
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Non-semisimple Levin–Wen models and Hermitian TQFTs from quantum (super)groups J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-18 Nathan Geer, Aaron D. Lauda, Bertrand Patureau-Mirand, Joshua Sussan
We develop the categorical context for defining Hermitian non-semisimple topological quantum field theories (TQFTs). We prove that relative Hermitian modular categories give rise to modified Hermitian Witten–Reshetikhin–Turaev TQFTs and provide numerous examples of these structures coming from the representation theory of quantum groups and quantum superalgebras. The Hermitian theory developed here
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Solutions of the Ginzburg–Landau equations concentrating on codimension-2 minimal submanifolds J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-13 Marco Badran, Manuel del Pino
We consider the magnetic Ginzburg–Landau equations on a closed manifold N $N$
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Tiling billards on triangle tilings, and interval exchange transformations J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-13 Paul Baird-Smith, Diana Davis, Elijah Fromm, Sumun Iyer
We consider the dynamics of light rays in triangle tilings where triangles are transparent and adjacent triangles have equal but opposite indices of refraction. We find that the behavior of a trajectory on a triangle tiling is described by an orientation-reversing three-interval exchange transformation on the circle, and that the behavior of all the trajectories on a given triangle tiling is described
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On the sheafyness property of spectra of Banach rings J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-13 Federico Bambozzi, Kobi Kremnizer
Let R $R$ be a non-Archimedean Banach ring, satisfying some mild technical hypothesis that we will specify later on. We prove that it is possible to associate to R $R$ a homotopical Huber spectrum Spa h ( R ) ${\rm Spa\,}^h(R)$ via the introduction of the notion of derived rational localization. The spectrum so obtained is endowed with a derived structural sheaf O Spa h ( R ) ${\mathcal {O}}_{{\rm
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A unified half-integral Erdős–Pósa theorem for cycles in graphs labelled by multiple abelian groups J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-13 J. Pascal Gollin, Kevin Hendrey, Ken-ichi Kawarabayashi, O-joung Kwon, Sang-il Oum
Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold if we restrict to odd cycles. However, in 1999, Reed proved an analogue for odd cycles by relaxing packing to half-integral packing. We prove a far-reaching generalisation of the theorem of Reed; if the edges of a
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Bott-integrable Reeb flows on 3-manifolds J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-13 Hansjörg Geiges, Jakob Hedicke, Murat Sağlam
This paper is devoted to studying a notion of Bott integrability for Reeb flows on contact 3-manifolds. We show, in analogy with work of Fomenko–Zieschang on Hamiltonian flows in dimension 4, that Bott-integrable Reeb flows exist precisely on graph manifolds. We also show that all S 1 $S^1$ -invariant contact structures on Seifert manifolds, as well as all contact structures on the 3-sphere, on the
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On the Σ-invariants of Artin groups satisfying the K(π,1)-conjecture J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-15 Marcos Escartín-Ferrer, Conchita Martínez-Perez
We consider Σ$\Sigma$-invariants of Artin groups that satisfy the K(π,1)$K(\pi,1)$-conjecture. These invariants determine the cohomological finiteness conditions of subgroups that contain the derived subgroup. We extend a known result for even Artin groups of FC-type, giving a sufficient condition for a character χ:AΓ→R$\chi:A_\Gamma \rightarrow \mathbb {R}$ to belong to Σn(AΓ,Z)$\Sigma ^n(A_\Gamma
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Riemann–Hilbert–Birkhoff inverse problem for semisimple flat F-manifolds and convergence of oriented associativity potentials J. Lond. Math. Soc. (IF 1.2) Pub Date : 2024-01-15 Giordano Cotti
In this paper, we address the problem of classification of quasi-homogeneous formal power series providing solutions of the oriented associativity equations. Such a classification is performed by introducing a system of monodromy local moduli on the space of formal germs of homogeneous semisimple flat F $F$ -manifolds. This system of local moduli is well defined on the complement of the strictly doubly
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Buildings, valuated matroids, and tropical linear spaces J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-28 Luca Battistella, Kevin Kühn, Arne Kuhrs, Martin Ulirsch, Alejandro Vargas
Affine Bruhat–Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of PGL $\mathrm{PGL}$ parameterizes flags of subspaces/lattices in or, equivalently, norms on a fixed finite-dimensional vector space, up to homothety. It has first been studied by Goldman and Iwahori as a piecewise-linear analogue of symmetric spaces. The space of seminorms compactifies
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Boundedness in families with applications to arithmetic hyperbolicity J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-28 Raymond van Bommel, Ariyan Javanpeykar, Ljudmila Kamenova
Motivated by conjectures of Demailly, Green–Griffiths, Lang and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to show the persistence of arithmetic hyperbolicity along field extensions for projective normal surfaces with non-zero irregularity. These results rely on the mild boundedness of semi-abelian varieties. We also introduce and
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Equivariant resolutions over Veronese rings J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-28 Ayah Almousa, Michael Perlman, Alexandra Pevzner, Victor Reiner, Keller VandeBogert
Working in a polynomial ring S = k [ x 1 , … , x n ] $S={\mathbf {k}}[x_1,\ldots ,x_n]$ , where k ${\mathbf {k}}$ is an arbitrary commutative ring with 1, we consider the d $d$ th Veronese subalgebras R = S ( d ) $R={S^{(d)}}$ , as well as natural R $R$ -submodules M = S ( ⩾ r , d ) $M={S^{({\geqslant r},{d})}}$ inside S $S$ . We develop and use characteristic-free theory of Schur functors associated
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The Cheeger problem in abstract measure spaces J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-26 Valentina Franceschi, Andrea Pinamonti, Giorgio Saracco, Giorgio Stefani
We consider nonnegative σ$\sigma$-finite measure spaces coupled with a proper functional P$P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space perimeter. Throughout the paper, the measure space will never be asked
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Characterization of the null energy condition via displacement convexity of entropy J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-19 Christian Ketterer
We characterize the null energy condition for an ( n + 1 ) $(n+1)$ -dimensional, time-oriented Lorentzian manifold in terms of convexity of the relative ( n − 1 ) $(n-1)$ -Renyi entropy along displacement interpolations on null hypersurfaces. More generally, we also consider Lorentzian manifolds with a smooth weight function and introduce the Bakry–Emery N $N$ -null energy condition that we characterize
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Large sums of high-order characters J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-19 Alexander P. Mangerel
Let χ $\chi$ be a primitive character modulo a prime q $q$ , and let δ > 0 $\delta > 0$ . It has previously been observed that if χ $\chi$ has large order d ⩾ d 0 ( δ ) $d \geqslant d_0(\delta)$ then χ ( n ) ≠ 1 $\chi (n) \ne 1$ for some n ⩽ q δ $n \leqslant q^{\delta}$ , in analogy with Vinogradov's conjecture on quadratic non-residues. We give a new and simple proof of this fact. We show, furthermore
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Semilinear elliptic Schrödinger equations with singular potentials and absorption terms J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-19 Konstantinos T. Gkikas, Phuoc-Tai Nguyen
Let Ω⊂RN$\Omega \subset \mathbb {R}^N$ (N⩾3$N \geqslant 3$) be a C2$C^2$ bounded domain and Σ⊂Ω$\Sigma \subset \Omega$ be a compact, C2$C^2$ submanifold without boundary, of dimension k$k$ with 0⩽k1$p>1$, we show that problem (P) admits several critical exponents in the sense that singular solutions exist in the subcritical cases (i.e. p$p$ is smaller than a critical exponent) and singularities are
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Drivers, hitting times, and weldings in Loewner's equation J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-20 Vlad Margarint, Tim Mesikepp
In addition to conformal weldings φ$\varphi$, simple curves γ$\gamma$ growing in the upper half plane generate driving functions ξ$\xi$ and hitting times τ$\tau$ through Loewner's differential equation. While the Loewner transform γ↦ξ$\gamma \mapsto \xi$ and its inverse ξ↦γ$\xi \mapsto \gamma$ have been carefully examined, less attention has been paid to the maps ξ↦τ↦φ$\xi \mapsto \tau \mapsto \varphi$
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On real Calabi–Yau threefolds twisted by a section J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-20 Diego Matessi
We study the mod 2 cohomology of real Calabi–Yau threefolds given by real structures that preserve the torus fibrations constructed by Gross. We extend the results of Castaño–Bernard–Matessi and Arguz–Prince to the case of real structures twisted by a Lagrangian section. In particular, we find exact sequences linking the cohomology of the real Calabi–Yau with the cohomology of the complex one. Applying
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The stochastic Schwarz lemma on Kähler manifolds by couplings and its applications J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-21 Myeongju Chae, Gunhee Cho, Maria Gordina, Guang Yang
We first provide a stochastic formula for the Carathéodory distance in terms of general Markovian couplings and prove a comparison result between the Carathéodory distance and the complete Kähler metric with a negative lower curvature bound using the Kendall–Cranston coupling. This probabilistic approach gives a version of the Schwarz lemma on complete noncompact Kähler manifolds with a further decomposition
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Arithmetics of homogeneous spaces over p-adic function fields J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-12-19 Nguyen Manh Linh
Let K $K$ be the function field of a smooth projective geometrically integral curve over a finite extension of Q p $\mathbb {Q}_p$ . Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local–global and weak approximation problems for homogeneous spaces of SL n , K $\textrm {SL}_{n,K}$ with geometric stabilizers extension of a group of multiplicative type by a unipotent
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Airy structures and deformations of curves in surfaces J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-11-27 W. Chaimanowong, P. Norbury, M. Swaddle, M. Tavakol
An embedded curve in a symplectic surface Σ ⊂ X $\Sigma \subset X$ defines a smooth deformation space B $\mathcal {B}$ of nearby embedded curves. A key idea of Kontsevich and Soibelman is to equip the symplectic surface X $X$ with a foliation in order to study the deformation space B $\mathcal {B}$ . The foliation, together with a vector space V Σ $V_\Sigma$ of meromorphic differentials on Σ $\Sigma$
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Steady Kähler–Ricci solitons on crepant resolutions of finite quotients of Cn J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-11-21 Olivier Biquard, Heather Macbeth
We prove the existence of steady Kähler–Ricci solitons on equivariant crepant resolutions of C n / G $\mathbb {C}^n/G$ , where G $G$ is a finite subgroup of S U ( n ) $SU(n)$ acting freely on C n $\mathbb {C}^n$ .
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One-dimensional sharp discrete Hardy–Rellich inequalities J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-11-19 Xia Huang, Dong Ye
In this paper, we establish discrete Hardy–Rellich inequalities on N$\mathbb {N}$ with Δℓ2$\Delta ^\frac{\ell }{2}$ and optimal constants, for any ℓ⩾1$\ell \geqslant 1$. As far as we are aware, these sharp inequalities are new for ℓ⩾3$\ell \geqslant 3$. Our approach is to use weighted equalities to get some sharp Hardy inequalities using shifting weights, then to settle the higher order cases by iteration
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The monotonicity and convexity of the incompressible rotational cavity flow J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-11-16 Jianfeng Cheng, Zhenlei Pei
This paper is concerned with the monotonicity and convexity of the incompressible rotational cavity flow past a fixed obstacle. More precisely, we first establish the single intersection property of the free boundary by the Serrin's under–over theorem, and prove the monotonicity of the free boundary with respect to the obstacle. If the obstacle is concave to the fluid, it is proved that the free boundary
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Mappings of generalized finite distortion and continuity J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-11-13 Anna Doležalová, Ilmari Kangasniemi, Jani Onninen
We study continuity properties of Sobolev mappings f ∈ W loc 1 , n ( Ω , R n ) $f \in W_{\mathrm{loc}}^{1,n} (\Omega , \mathbb {R}^n)$ , n ⩾ 2 $n \geqslant 2$ , that satisfy the following generalized finite distortion inequality
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Primes with a missing digit: Distribution in arithmetic progressions and an application in sieve theory J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-11-13 Kunjakanan Nath
We prove Bombieri–Vinogradov type theorems for primes with a missing digit in their b$b$-adic expansion for some large positive integer b$b$. The proof is based on the circle method, which relies on the Fourier structure of the integers with a missing digit and the exponential sums over primes in arithmetic progressions. Combining our results with the semi-linear sieve, we obtain an upper bound and
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Analytic ranks of automorphic L-functions and Landau–Siegel zeros J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-11-11 Hung M. Bui, Kyle Pratt, Alexandru Zaharescu
We relate the study of Landau–Siegel zeros to the ranks of Jacobians J 0 ( q ) $J_0(q)$ of modular curves for large primes q $q$ . By a conjecture of Brumer–Murty, the rank should be equal to half of the dimension. Equivalently, almost all newforms of weight two and level q $q$ have analytic rank ⩽ 1 $\leqslant 1$ . We show that either Landau–Siegel zeros do not exist, or that, for wide ranges of q
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Presenting the cohomology of a Schubert variety: Proof of the minimality conjecture J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-11-03 Avery St. Dizier, Alexander Yong
A minimal presentation of the cohomology ring of the flag manifold G L n / B $GL_n/B$ was given in A. Borel (1953). This presentation was extended by E. Akyildiz–A. Lascoux–P. Pragacz (1992) to a nonminimal one for all Schubert varieties. Work of V. Gasharov–V. Reiner (2002) gave a short, that is, polynomial-size, presentation for a subclass of Schubert varieties that includes the smooth ones. In V
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Adelic Rogers integral formula J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-31 Seungki Kim
We formulate and prove the extension of the Rogers integral formula (Rogers [Acta Math. 94 (1955), 249–287]) to the adeles of number fields. We also prove the second moment formulas for a few important cases, enabling a number of classical and recent applications of the formula to extend immediately to any number field.
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Newton–Okounkov bodies and symplectic embeddings into nontoric rational surfaces J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-31 Julian Chaidez, Ben Wormleighton
We develop new methods of both constructing and obstructing symplectic embeddings into nontoric rational surfaces using the theory of Newton–Okoukov bodies. Applications include sharp embedding results for concave toric domains into nontoric rational surfaces, and new cases of nonexistence for infinite staircases in the nontoric setting.
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Moduli of polarised Enriques surfaces — Computational aspects J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-25 Mathieu Dutour Sikirić, Klaus Hulek
Moduli spaces of (polarised) Enriques surfaces can be described as open subsets of modular varieties of orthogonal type. It was shown by Gritsenko and Hulek that there are, up to isomorphism, only finitely many different moduli spaces of polarised Enriques surfaces. Here, we investigate the possible arithmetic groups and show that there are exactly 87 such groups up to conjugacy. We also show that
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Generating numbers of rings graded by amenable and supramenable groups J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-23 Karl Lorensen, Johan Öinert
A ring R$R$ has unbounded generating number (UGN) if, for every positive integer n$n$, there is no R$R$-module epimorphism Rn→Rn+1$R^n\rightarrow R^{n+1}$. For a ring R=⨁g∈GRg$R=\bigoplus _{g\in G} R_g$ graded by a group G$G$ such that the base ring R1$R_1$ has UGN, we identify several sets of conditions under which R$R$ must also have UGN. The most important of these are: (1) G$G$ is amenable, and
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Inductive and divisional posets J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-22 Roberto Pagaria, Maddalena Pismataro, Tan Nhat Tran, Lorenzo Vecchi
We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we introduce and study the notion of inductive posets and their superclass of divisional posets. It then motivates us to define the so-called inductive and divisional abelian (Lie group) arrangements, whose posets of layers serve
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Apéry extensions J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-20 Vasily Golyshev, Matt Kerr, Tokio Sasaki
The Apéry numbers of Fano varieties are asymptotic invariants of their quantum differential equations. In this paper, we initiate a program to exhibit these invariants as (mirror to) limiting extension classes of higher cycles on the associated Landau–Ginzburg (LG) models — and thus, in particular, as periods. We also construct an Apéry motive, whose mixed Hodge structure is shown, as an application
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G-crossed braided zesting J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-18 Colleen Delaney, César Galindo, Julia Plavnik, Eric C. Rowell, Qing Zhang
For a finite group G $G$ , a G $G$ -crossed braided fusion category is a G $G$ -graded fusion category with additional structures, namely, a G $G$ -action and a G $G$ -braiding. We develop the notion of G $G$ -crossed braided zesting: an explicit method for constructing new G $G$ -crossed braided fusion categories from a given one by means of cohomological data associated with the invertible objects
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Random generation of associative algebras J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-17 Damian Sercombe, Aner Shalev
There has been considerable interest in recent decades in questions of random generation of finite and profinite groups and finite simple groups in particular. In this paper, we study similar notions for finite and profinite associative algebras. Let k = F q $k=\mathbb {F}_q$ be a finite field. Let A $A$ be a finite-dimensional, associative, unital algebra over k $k$ . Let P ( A ) $P(A)$ be the probability
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On Waring's problem: Beyond Freĭman's theorem J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-16 Jörg Brüdern, Trevor D. Wooley
Let k i ∈ N $k_i\in {\mathbb {N}}$ ( i ⩾ 1 ) $(i\geqslant 1)$ satisfy 2 ⩽ k 1 ⩽ k 2 ⩽ ⋯ $2\leqslant k_1\leqslant k_2\leqslant \cdots$ . Freĭman's theorem shows that when j ∈ N $j\in {\mathbb {N}}$ , there exists s = s ( j ) ∈ N $s=s(j)\in {\mathbb {N}}$ such that all large integers n $n$ are represented in the form n = x 1 k j + x 2 k j + 1 + ⋯ + x s k j + s − 1 $n=x_1^{k_j}+x_2^{k_{j+1}}+\cdots +x_s^{k_{j+s-1}}$
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ABHY Associahedra and Newton polytopes of F-polynomials for cluster algebras of simply laced finite type J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-15 Véronique Bazier-Matte, Nathan Chapelier-Laget, Guillaume Douville, Kaveh Mousavand, Hugh Thomas, Emine Yildirim
A new construction of the associahedron was recently given by Arkani-Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their construction (suitably understood) can be applied to construct generalized associahedra of any simply laced Dynkin type. Unexpectedly, we also show that this same construction produces Newton polytopes for all the F $F$ -polynomials
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The uniqueness theorem for Gysin coherent characteristic classes of singular spaces J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-13 Markus Banagl, Dominik J. Wrazidlo
We establish a general computational scheme designed for a systematic computation of characteristic classes of singular complex algebraic varieties that satisfy a Gysin axiom in a transverse setup. This scheme is explicitly geometric and of a recursive nature terminating on genera of explicit characteristic subvarieties that we construct. It enables us, for example, to apply intersection theory of
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Tropical vertex and real enumerative geometry J. Lond. Math. Soc. (IF 1.2) Pub Date : 2023-10-13 Eugenii Shustin
We show that the commutator relations in the refined tropical vertex group can be expressed via the enumeration of suitable real rational curves in toric surfaces.