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Geometric analysis of $1+1$ dimensional quasilinear wave equations Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Leonardo Enrique Abbrescia, Willie Wai Yeung Wong
We prove global well-posedness of the initial value problem for a class of variational quasilinear wave equations, in one spatial dimension, with initial data that is not necessarily small. Key to our argument is a form of quasilinear null condition (a “nilpotent structure”) that persists for our class of equations even in the large data setting. This in particular allows us to prove global wellposedness
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Equivariant sheaves on loop spaces Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Sergey Arkhipov, Sebastian Ørsted
Let $X$ be an affine, smooth, and Noetherian scheme over $\mathbb{C}$ acted on by an affine algebraic group $G$. Applying the technique developed in $\href{https://doi.org/10.48550/arXiv.1807.03266}{[3, }\href{ https://doi.org/10.48550/arXiv.1812.03583}{4]}$, we define a dg‑model for the derived category of dg‑modules over the dg‑algebra of differential forms $\Omega_X$ on $X$ equivariant with respect
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Continuity of the gradient of the fractional maximal operator on $W^{1,1} (\mathbb{R}^d)$ Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 David Beltran, Cristian González-Riquelme, José Madrid, Julian Weigt
We establish that the map $f \mapsto {\lvert \nabla \mathcal{M}_\alpha f \rvert}$ is continuous from $W^{1,1} (\mathbb{R}^d)$ to $L^q (\mathbb{R}^d)$, where $\alpha \in (0, d), q = \frac{d}{d-\alpha}$ and $M_\alpha$ denotes either the centered or non-centered fractional Hardy–Littlewood maximal operator. In particular, we cover the cases $d \gt 1$ and $\alpha \in (0, 1)$ in full generality, for which
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Stein-fillable open books of genus one that do not admit positive factorisations Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Vitalijs Brejevs, Andy Wand
We construct an infinite family of genus one open book decompositions supporting Stein-fillable contact structures and show that their monodromies do not admit positive factorisations. This extends a line of counterexamples in higher genera and establishes that a correspondence between Stein fillings and positive factorisations only exists for planar open book decompositions.
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Annihilators of $D$-modules in mixed characteristic Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Rankeya Datta, Nicholas Switala, Wenliang Zhang
Let $R$ be a polynomial or formal power series ring with coefficients in a DVR $V$ of mixed characteristic with a uniformizer $\pi$. We prove that the $R$-module annihilator of any nonzero $\mathcal{D}(R,V)$-module is either zero or is generated by a power of $\pi$. In contrast to the equicharacteristic case, nonzero annihilators can occur; we give an example of a top local cohomology module of the
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A Riemannian metric on hyperbolic components Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Yan Mary He, Hongming Nie
We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree at least $2$ rational maps in one complex variable. Our metric is constructed by considering the measure-theoretic entropy of a rational map with respect to some equilibrium state.
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Zero–one laws for eventually always hitting points in rapidly mixing systems Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Dmitry Kleinbock, Ioannis Konstantoulas, Florian K. Richter
In this work we study the set of eventually always hitting points in shrinking target systems. These are points whose long orbit segments eventually hit the corresponding shrinking targets for all future times. We focus our attention on systems where translates of targets exhibit near perfect mutual independence, such as Bernoulli schemes and the Gauß map. For such systems, we present tight conditions
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An example of non-Kähler Calabi–Yau fourfold Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Nam-Hoon Lee
We show that there exists a non-Kähler Calabi–Yau fourfold, constructing an example by smoothing a normal crossing variety.
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Extendability of automorphisms of K3 surfaces Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Yuya Matsumoto
A K3 surface $X$ over a $p$-adic field $K$ is said to have good reduction if it admits a proper smooth model over the ring of integers of $K$. Assuming this, we say that a subgroup $G$ of $\operatorname{Aut}(X)$ is extendable if $X$ admits a proper smooth model equipped with $G$-action (compatible with the action on $X$). We show that $G$ is extendable if it is of finite order prime to $p$ and acts
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Generalized Price’s law on fractional-order asymptotically flat stationary spacetimes Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Katrina Morgan, Jared Wunsch
We obtain estimates on the rate of decay of a solution to the wave equation on a stationary spacetime that tends to Minkowski space at a rate $O ({\lvert x \rvert}^{-\kappa}), \kappa \in (1,\infty) \backslash \mathbb{N}$. Given suitably smooth and decaying initial data, we show a wave locally enjoys the decay rate $O(t^{-\kappa-2+\epsilon})$.
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Properness of the global-to-local map for algebraic groups with toric connected component and other finiteness properties Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Andrei S. Rapinchuk, Igor A. Rapinchuk
This is a companion paper to $\href{ https://doi.org/10.1016/j.jnt.2021.07.001}{[29]}$, where we proved the finiteness of the Tate–Shafarevich group for an arbitrary torus $T$ over a finitely generated field $K$ with respect to any divisorial set $V$ of places of $K$. Here, we extend this result to any $K$-group $D$ whose connected component is a torus (for the same $V$), and as a consequence obtain
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A theorem on Hermitian rank and mapping problems Math. Res. Lett. (IF 1.0) Pub Date : 2023-12-15 Ming Xiao
In this paper, we first prove a Huang’s lemma type result. Then we discuss its applications in studying rigidity problems of mappings into indefinite hyperbolic spaces and bounded symmetric domains.
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A finiteness property of postcritically finite unicritical polynomials Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Robert L. Benedetto, Su-Ion Ih
Let $k$ be a number field with algebraic closure $\overline{k}$, and let $S$ be a finite set of places of $k$ containing all the archimedean ones. Fix $d \geq 2$ and $\alpha \in \overline{k}$ such that the map $z \mapsto z^d + \alpha$ is not postcritically finite. Assuming a technical hypothesis on $\alpha$, we prove that there are only finitely many parameters $c \in \overline{k}$ for which $z \mapsto
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Metrics of constant negative scalar-Weyl curvature Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Giovanni Catino
Extending Aubin’s construction of metrics with constant negative scalar curvature, we prove that every $n$-dimensional closed manifold admits a Riemannian metric with constant negative scalar-Weyl curvature, that is, $R + t {\lvert W \rvert}, t \in \mathbb{R}$. In particular, there are no topological obstructions for metrics with $\varepsilon$-pinched Weyl curvature and negative scalar curvature.
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Affine symmetries in quantum cohomology: corrections and new results Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Pierre-Emmanuel Chaput, Nicolas Perrin
In [$\href{https://dx.doi.org/10.4310/MRL.2009.v16.n1.a2}{\textrm{CMP09}}$] a general formula was given for the multiplication by some special Schubert classes in the quantum cohomology of any homogeneous space. Although this formula is true in the non equivariant setting, the stated equivariant version is wrong. We provide correction for the equivariant formula, thus giving a correct argument for
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Positive currents on non-kählerian surfaces Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Ionuţ Chiose, Matei Toma
We propose a classification of non-kählerian surfaces from a dynamical point of view and show how the known non-kählerian surfaces fit into it.
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Local and global densities for Weierstrass models of elliptic curves Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 John E. Cremona, Mohammad Sadek
We prove local results on the p-adic density of elliptic curves over $\mathbb{Q}_p$ with different reduction types, together with global results on densities of elliptic curves over $\mathbb{Q}$ with specified reduction types at one or more (including infinitely many) primes. These global results include: the density of integral Weierstrass equations which are minimal models of semistable elliptic
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Mather classes of Schubert varieties via small resolutions Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Minyoung Jeon
We express Schubert expansions of the Chern–Mather classes for Schubert varieties in the even orthogonal Grassmannians via integrals involving Pfaffians and pushforward of the small resolutions in the sense of Intersection Cohomology (IH) constructed by Sankaran and Vanchinathan, instead of the Nash blowup. The equivariant localization is employed to show the way of computing the integrals. As byproducts
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On the distribution of multiplicatively dependent vectors Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Sergei V. Konyagin, Min Sha, Igor E. Shparlinski, Cameron L. Stewart
In this paper, we study the distribution of multiplicatively dependent vectors. For example, although they have zero Lebesgue measure, they are everywhere dense both in $\mathbb{R}^n$ and $\mathbb{C}^n$. We also study this property in a more detailed manner by considering the covering radius of such vectors.
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Convexity of the weighted Mabuchi functional and the uniqueness of weighted extremal metrics Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Abdellah Lahdili
We prove the uniqueness, up to a pull-back by an element of a suitable subgroup of complex automorphisms, of the weighted extremal Kähler metrics on a compact Kähler manifold introduced in our previous work [$\href{https://doi.org/10.1112/plms.12255}{31}]$. This extends a result by Berman–Berndtsson [$\href{https://doi.org/10.1090/jams/880}{7}$] and Chen–Paun–Zeng [$\href{https://arxiv.org/pdf/1506
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Counting quintic fields with genus number one Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Kevin J. McGown, Frank Thorne, Amanda Tucker
We prove several results concerning genus numbers of quintic fields: we compute the proportion of quintic fields with genus number one; we prove that a positive proportion of quintic fields have arbitrarily large genus number; and we compute the average genus number of quintic fields. All of these results also hold when restricted to $S_5$-quintic fields only.
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Rigidity of rationally connected smooth projective varieties from dynamical viewpoints Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Sheng Meng, Guolei Zhong
Let $X$ be a rationally connected smooth projective variety of dimension $n$. We show that $X$ is a toric variety if and only if $X$ admits an int-amplified endomorphism with totally invariant ramification divisor. We also show that $X \cong (\mathbb{P}^1)^{\times n}$ if and only if $X$ admits a surjective endomorphism $f$ such that the eigenvalues of $f^\ast \vert_{\mathrm{N}^1(X)}$ (without counting
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Existence of an exotic plane in an acylindrical 3-manifold Math. Res. Lett. (IF 1.0) Pub Date : 2023-09-13 Yongquan Zhang
Let $P$ be a geodesic plane in a convex cocompact, acylindrical hyperbolic $3$-manifold $M$. Assume that $P^\ast = M^\ast \cap P$ is nonempty, where $M^\ast$ is the interior of the convex core of $M$. Does this condition imply that $P$ is either closed or dense in $M$? A positive answer would furnish an analogue of Ratner’s theorem in the infinite volume setting. In [$\href{https://doi.org/10.1215
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Hodge symmetry for rigid varieties via $\log$ hard Lefschetz Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 Piotr Achinger
Motivated by a question of Hansen and Li, we show that a smooth and proper rigid analytic space $X$ with projective reduction satisfies Hodge symmetry in the following situations: (1) the base non-archimedean field $K$ is of residue characteristic zero, (2) $K$ is $p$-adic and $X$ has good ordinary reduction, (3) $K$ is $p$-adic and $X$ has “combinatorial reduction.” We also reprove a version of their
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Higher $\operatorname{Ext}$-groups in the triple product case Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 Li Cai, Yangyu Fan
In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product case.
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Contractibility of space of stability conditions on the projective plane via global dimension function Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 Yu-Wei Fan, Chunyi Li, Wanmin Liu, Yu Qiu
We compute the global dimension function $\operatorname{gldim}$ on the principal component $\operatorname{Stab}^\dagger (\mathbb{P}^2)$ of the space of Bridgeland stability conditions on $\mathbb{P}^2$. It admits $2$ as the minimum value and the preimage $\operatorname{gldim}^{-1} (2)$ is contained in the closure $\overline{\operatorname{Stab}^{\operatorname{Geo}} \mathbb{P}^2}$ of the subspace consisting
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On Kakeya maps with regularity assumptions Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 Yuqiu Fu, Shengwen Gan
In $\mathbb{R}^n$, we parametrize Kakeya sets using Kakeya maps. A Kakeya map is defined to be a map\[\phi : B^{n-1}(0, 1) \times [0, 1] \to \mathbb{R}^n, \qquad (v, t) \mapsto (c(v) + tv, t),\]where $c : B^{n-1} (0, 1) \to \mathbb{R}^{n-1}$. The associated Kakeya set is defined to be $K := \operatorname{Im}(\phi)$. We show that the Kakeya set $K$ has positive measure if either one of the following
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The Surface Group Conjectures for groups with two generators Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 Giles Gardam, Dawid Kielak, Alan D. Logan
The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups. We resolve these conjectures in the two generator case. More generally, we prove that every two-generator one-relator group with every infinite-index subgroup free is itself either free or a surface group.
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On type II degenerations of hyperkähler manifolds Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 D. Huybrechts, M. Mauri
We give a simple argument to prove Nagai’s conjecture for type II degenerations of compact hyperkähler manifolds and cohomology classes of middle degree. Under an additional assumption, the techniques yield the conjecture in arbitrary degree. This would complete the proof of Nagai’s conjecture in general, as it was proved already for type I degenerations by Kollár, Laza, Saccà, and Voisin [10] and
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Linear subspaces of minimal codimension in hypersurfaces Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 David Kazhdan, Alexander Polishchuk
Let $\mathbf{k}$ be a perfect field and let $X \subset \mathbb{P}^N$ be a hypersurface of degree $d$ defined over $\mathbf{k}$ and containing a linear subspace $L$ defined over $\overline{\mathbf{k}}$ with $\operatorname{codim}_{\mathbb{P}^N} L = r$. We show that $X$ contains a linear subspace $L_0$ defined over $\mathbf{k}$ with $\operatorname{codim}_{\mathbb{P}^N} L \leq dr$. We conjecture that the
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A note on singular Hermitian Yang–Mills connections Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 Yang Li
We give an example of a homogeneous reflexive sheaf over $\mathbb{C}^3$ which admits a non-conical Hermitian Yang–Mills connection. This is expected to model bubbling phenomenon along complex codimension $2$ submanifolds when the Fueter section takes zero value.
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Blowing up extremal Poincaré type manifolds Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 Lars Martin Sektnan
We prove a version of the Arezzo–Pacard–Singer blow-up theorem in the setting of Poincaré type metrics. We apply this to give new examples of extremal Poincaré type metrics. A key feature is an additional obstruction which has no analogue in the compact case. This condition is conjecturally related to ensuring the metrics remain of Poincaré type.
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Derived categories of Quot schemes of locally free quotients via categorified Hall products Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 Yukinobu Toda
We prove Qingyuan Jiang’s conjecture on semiorthogonal decompositions of derived categories of Quot schemes of locally free quotients. The author’s result on categorified Hall products for Grassmannian flips is applied to prove the conjecture.
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Non-isogenous elliptic curves and hyperelliptic jacobians Math. Res. Lett. (IF 1.0) Pub Date : 2023-06-21 Yuri G. Zarhin
Let $K$ be a field of characteristic different from $2$, $\overline{K}$ its algebraic closure. Let $n \geq 3$ be an odd prime such that $2$ is a primitive root modulo $n$. Let $f(x)$ and $h(x)$ be degree $n$ polynomials with coefficients in $K$ and without repeated roots. Let us consider genus $(n-1)/2$ hyperelliptic curves $C_f : y^2 = f(x)$ and $C_h : y^2 = h(x)$, and their jacobians $J(C_f)$ and
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Diagrams of $\star$-trisections Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Román Aranda, Jesse Moeller
In this note we provide a generalization for the definition of a trisection of a $4$-manifold with boundary. We demonstrate the utility of this more general definition by finding a trisection diagram for the Cacime Surface, and also by finding a trisection-theoretic way to perform logarithmic surgery. In addition, we describe how to perform $1$-surgery on closed trisections. The insight gained from
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Complex Monge–Ampère equations with solutions in finite energy classes Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Duc Thai Do, Duc-Viet Vu
We characterize the class of probability measures on a compact Kähler manifold such that the associated Monge–Ampère equation has a solution of finite pluricomplex energy. Our results are also valid in the big cohomology class setting.
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Almost Kähler Kodaira–Spencer problem Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Tom Holt, Weiyi Zhang
We show that the almost complex Hodge number $h^{0,1}$ varies with different choices of almost Kähler metrics. This answers the almost Kähler version of a question of Kodaira and Spencer.
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Internal stabilization for KdV-BBM equation on a periodic domain Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Melek Jellouli, Moez Khenissi
We consider the nonlinear damped KdV‑BBM equation on the torus. We shows the global existence of the solution, as well as its convergence in time towards an analytical function. This analyticity property allows the application of unique continuation results to show that the limit function is a constant.
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Continuous time soliton resolution for two-bubble equivariant wave maps Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Jacek Jendrej, Andrew Lawrie
We consider the energy-critical wave maps equation $\mathbb{R}^{1+2} \to \mathbb{S}^2$ in the equivariant case. We prove that if a wave map decomposes, along a sequence of times, into a superposition of at most two rescaled harmonic maps (bubbles) and radiation, then such a decomposition holds for continuous time. We deduce, as a consequence of sequential soliton resolution results of Côte [5], and
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Endpoint $\ell^r$ improving estimates for prime averages Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi
Let $\Lambda$ denote von Mangoldt’s function, and consider the averages\[A_N f(x) = \frac{1}{N} \sum_{1 \leq n \leq N} f(x-n) \Lambda (n).\]We prove sharp $\ell^p$-improving for these averages, and sparse bounds for the maximal function. The simplest inequality is that for sets $F,G \subset [0,N]$ there holds\[N^{-1} \langle A_N 1_F , 1_G \rangle \ll\dfrac{\lvert F \rvert \cdot \lvert G \rvert }{N^2}{\left(
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Representations of surface groups with universally finite mapping class group orbit Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Brian Lawrence, Daniel Litt
Let $\Sigma_{g,n}$ be the orientable genus $g$ surface with $n$ punctures, where $2 - 2_g - n \lt 0$. Let\[\rho : \pi_1 (\Sigma_{g,n}) \to GL_m (\mathbb{C})\]be a representation. Suppose that for each finite covering map $f : \Sigma_{g^\prime, n^\prime} \to \Sigma_{g,n}$ the orbit of (the isomorphism class of) $f^\ast (\rho)$ under the mapping class group $MCG (\Sigma_{g^\prime, n^\prime})$ of $\Sigma_{g^\prime
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Boundary branch divisor of toroidal compactification Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Shouhei Ma
We prove that any toroidal compactification of arithmetic quotient of Hermitian symmetric domain has no boundary branch divisor, in the setting where the algebraic group is of adjoint type.
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Negative Sasakian structures on simply-connected $5$-manifolds Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Vicente Muñoz, Matthias Schütt, Aleksy Tralle
We study several questions on the existence of negative Sasakian structures on simply connected rational homology spheres and on Smale–Barden manifolds of the form $\#_k (S^2 \times S^3)$. First, we prove that any simply connected rational homology sphere admitting positive Sasakian structures also admits a negative one. This result answers the question, posed by Boyer and Galicki in their book [3]
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On the projective derivative cocycle for circle diffeomorphisms Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Andrés Navas, Mario Ponce
We study the projective derivative as a cocycle of Möbius transformations over groups of circle diffeomorphisms. By computing precise expressions for this cocycle, we obtain several results about reducibility and almost reducibility to a cocycle of rotations. We also introduce an extension of this cocycle to the diagonal action on the $3$-torus for which we generalize the previous results.
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Persistence of the Brauer–Manin obstruction on cubic surfaces Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Carlos Rivera, Bianca Viray
Let $X$ be a cubic surface over a global field $k$. We prove that a Brauer–Manin obstruction to the existence of $k$-points on $X$ will persist over every extension $L/k$ with degree relatively prime to $3$. In other words, a cubic surface has nonempty Brauer set over $k$ if and only if it has nonempty Brauer set over some extension $L/k$ with $3 \nmid [L:k]$. Therefore, the conjecture of Colliot–Thélène
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Kodaira dimension and zeros of holomorphic one-forms, revisited Math. Res. Lett. (IF 1.0) Pub Date : 2023-05-04 Mads Bach Villadsen
We give a new proof that every holomorphic one-form on a smooth complex projective variety of general type must vanish at some point, first proven by Popa and Schnell using generic vanishing theorems for Hodge modules. Our proof relies on Simpson’s results on the relation between rank one Higgs bundles and local systems of one-dimensional complex vector spaces, and the structure of the cohomology jump
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Existence and uniqueness of stationary solutions in $5$-dimensional minimal supergravity Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Aghil Alaee, Marcus Khuri, Hari Kunduri
We study the problem of stationary bi-axially symmetric solutions of the $5$-dimensional minimal supergravity equations. Essentially all possible solutions with nondegenerate horizons are produced, having the allowed horizon cross-sectional topologies of the sphere $S^3$, ring $S^1 \times S^2$, and lens $L(p, q)$, as well as the three different types of asymptotics. The solutions are smooth apart from
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Polya enumeration theorems in algebraic geometry Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Gilyoung Cheong
We generalize a formula due to Macdonald that relates the singular Betti numbers of $X^n / G$ to those of $X$, where $X$ is a compact manifold and $G$ is any subgroup of the symmetric group $S_n$ acting on $X^n$ by permuting coordinates. Our result is completely axiomatic: in a general setting, given an endomorphism on the cohomology $H^\bullet (X)$, it explains how we can explicitly relate the Lefschetz
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A note on blowup limits in 3d Ricci flow Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Beomjun Choi, Robert Haslhofer
We prove that Perelman’s ancient ovals occur as blowup limit in 3d Ricci flow through singularities if and only if there is an accumulation of spherical singularities.
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Orderability of homology spheres obtained by Dehn filling Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Xinghua Gao
In this paper, we develop a method for constructing left-orders on the fundamental groups of rational homology $3$-spheres. We begin by constructing the holonomy extension locus of a rational homology solid torus $M$, which encodes the information about peripherally hyperbolic $\widetilde{\mathrm{PSL}_2 \mathbb{R}}$ representations of $\pi_1 (M)$. Plots of the holonomy extension loci of many rational
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On quaternionic rigid meromorphic cocyles Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Lennart Gehrmann
Recently, Darmon and Vonk initiated the theory of rigid meromorphic cocycles for the group $\mathbb{SL}_2 (\mathbb{Z}[1/p])$. One of their major results is the algebraicity of the divisor associated to such a cocycle. We generalize the result to the setting of $\mathfrak{p}$-arithmetic subgroups of inner forms of $\mathbb{SL}_2$ over arbitrary number fields. The method of proof differs from the one
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Counting ancient solutions on a strip with exponential growth Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Feng Gui
We study the ancient solutions of parabolic equations on an infinite strip. We show that any polynomial growth ancient solution for a class of parabolic equations must be constant. Furthermore, we show that the vector space of ancient solutions that grow slower than a fixed exponential order is of finite dimension.
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Real-analytic coordinates for smooth strictly pseudoconvex CR-structures Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 I. Kossovskiy, D. Zaitsev
For a smooth strictly pseudoconvex hypersurface in a complex manifold, we give a necessary and sufficient condition for being CR-diffeomorphic to a real-analytic CR manifold. Our condition amounts to a holomorphic extension property for the canonically associated function expressing $2$-jets of the formal Segre varieties in terms of their $1$-jets. We also express this condition in equivalent terms
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Deformation of Hermitian metrics Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Man-Chun Lee, Ka-Fai Li
In this work, we study the deformation of Hermitian metrics and the respective Chern curvature tensors. By adapting the conformal perturbation method of Aubin and Ehrlich to Hermitian setting, we prove that Hermitian metrics with quasi-positive (resp. quasi-negative) second Chern–Ricci curvature is conformal to a Hermitian metric with positive (resp. negative) second Chern–Ricci curvature.
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Semi-infinite Plücker relations and arcs over toric degeneration Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Ievgen Makedonskyi
We study the algebra of Weyl modules in types $A$ and $C$ using the methods of arcs over toric degenerations and functional realization of dual space. We compute the generators and relations of this algebra and construct its basis.
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Extending vector bundles on curves Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Siddharth Mathur
Given a curve in a (smooth) projective variety $C \subset X$ over an algebraically closed field $k$, we show that a vector bundle $V$ on $C$ can be extended to a ($\mu$-stable) vector bundle on $X$ if rank$(V) \geq \dim(X)$ and $\operatorname{det}(V)$ extends to $X$.
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Counting twisted Higgs bundles Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Sergey Mozgovoy, Ronan O’Gorman
We prove an explicit formula, conjectured earlier by the first author, counting semistable twisted Higgs bundles over a smooth projective curve.
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Convex hull property for ancient harmonic map heat flows Math. Res. Lett. (IF 1.0) Pub Date : 2023-04-21 Chiung-Jue Anna Sung
For an ancient solution u to the harmonic map heat flow from a complete manifold $M$ into a Cartan–Hadamard manifold $N$ with curvature bounded between two negative constants, we show that the image of $u$ is contained in the convex hull of its intersection with the ideal boundary of $N$ together with at most $k$ interior points in $N$, where $k$ is the dimension of the space of bounded ancient solutions
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Symplectic realizations of holomorphic Poisson manifolds Math. Res. Lett. (IF 1.0) Pub Date : 2023-02-23 Damien Broka, Ping Xu
Symplectic realization is a longstanding problem which can be traced back to Sophus Lie. In this paper, we present an explicit solution to this problem for an arbitrary holomorphic Poisson manifold. More precisely, for any holomorphic Poisson manifold $(\mathscr{X},\pi)$ with underlying real smooth manifold $X$, we prove that there exists a holomorphic symplectic structure in a neighborhood $Y$ of
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Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions Math. Res. Lett. (IF 1.0) Pub Date : 2023-02-23 Jann-Long Chern, Maria Gualdani
We are concerned with the uniqueness of weak solution to the spatially homogeneous Landau equation with Coulomb interactions under the assumption that the solution is bounded in the space $L^\infty (0, T, L^p (\mathbb{R}^3))$ for some $p \gt 3/2$. The proof uses a weighted Poincaré–Sobolev inequality recently introduced in [11].