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Weak approximation on Châtelet surfaces manuscripta math. (IF 0.6) Pub Date : 2024-03-18 Masahiro Nakahara, Samuel Roven
We study weak approximation for Châtelet surfaces over number fields when all singular fibers are defined over rational points. We consider Châtelet surfaces which satisfy weak approximation over every finite extension of the ground field. We prove many of these results by showing that the Brauer–Manin obstruction vanishes, then apply results of Colliot-Thélène, Sansuc, and Swinnerton-Dyer.
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Liouville theorem for exponentially harmonic functions on Riemannian manifolds with compact boundary manuscripta math. (IF 0.6) Pub Date : 2024-03-16 Xinrong Jiang, Jianyi Mao
In this note, we derive a Yau type gradient estimate for positive exponentially harmonic functions on Riemannian manifolds with compact boundary. As its application, we obtain a Liouville type theorem.
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Gromov hyperbolicity and unbounded uniform domains manuscripta math. (IF 0.6) Pub Date : 2024-03-16 Qingshan Zhou, Yuehui He, Antti Rasila, Tiantian Guan
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Partial regularity for minimizers of a class of discontinuous Lagrangians manuscripta math. (IF 0.6) Pub Date : 2024-03-14 Roberto Colombo
We study a one-dimensional Lagrangian problem including the variational reformulation, derived in a recent work of Ambrosio–Baradat–Brenier, of the discrete Monge–Ampère gravitational model, which describes the motion of interacting particles whose dynamics is ruled by the optimal transport problem. The more general action-type functional we consider contains a discontinuous potential term related
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Hodge numbers of O’Grady 6 via Ngô strings manuscripta math. (IF 0.6) Pub Date : 2024-03-13 Ben Wu
We give an alternative computation of the Betti and Hodge numbers for manifolds of OG6 type using the method of Ngô Strings introduced by de Cataldo, Rapagnetta, and Saccà.
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Poisson commutative subalgebras associated with a Cartan subalgebra manuscripta math. (IF 0.6) Pub Date : 2024-03-13 Oksana S. Yakimova
Let \({\mathfrak g}\) be a reductive Lie algebra and \(\mathfrak t\subset \mathfrak g\) a Cartan subalgebra. The \(\mathfrak t\)-stable decomposition \({\mathfrak g}=\mathfrak t\oplus {\mathfrak m}\) yields a bi-grading of the symmetric algebra \({\mathcal {S}}({\mathfrak g})\). The subalgebra \({\mathcal {Z}}_{({\mathfrak g},\mathfrak t)}\) generated by the bi-homogenous components of the symmetric
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Weights for compact connected Lie groups manuscripta math. (IF 0.6) Pub Date : 2024-03-09 Radha Kessar, Gunter Malle, Jason Semeraro
Let \(\ell \) be a prime. If \(\textbf{G}\) is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from \(\ell \), and \(\ell \) is a good prime for \(\textbf{G}\), we show that the number of weights of the \(\ell \)-fusion system of \(\textbf{G}\) is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification
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Upper bounds for the critical values of homology classes of loops manuscripta math. (IF 0.6) Pub Date : 2024-03-02 Hans-Bert Rademacher
In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of compact manifolds carrying a Riemannian or Finsler metric of positive Ricci curvature. In particular it follows that a shortest closed geodesic on a compact and simply-connected n-dimensional manifold of positive Ricci curvature \(\text {Ric}\ge n-1\) has length \(\le n \pi .\)
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Diameter estimates for surfaces in conformally flat spaces manuscripta math. (IF 0.6) Pub Date : 2024-03-01 Marco Flaim, Christian Scharrer
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Singular Yamabe problem for scalar flat metrics on the sphere manuscripta math. (IF 0.6) Pub Date : 2024-01-24 Aram L. Karakhanyan
Let \(\Omega \) be a domain on the unit n-sphere \( {\mathbb {S}}^n\) and \( \overset{{\,}_\circ }{g}\) the standard metric of \({\mathbb {S}}^n\), \(n\ge 3\). We show that there exists a conformal metric g with vanishing scalar curvature \(R(g)=0\) such that \((\Omega , g)\) is complete if and only if the Bessel capacity \({\mathcal {C}}_{\alpha , q}({\mathbb {S}}^n\setminus \Omega )=0\), where \(\alpha
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Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kähler manifolds manuscripta math. (IF 0.6) Pub Date : 2024-01-21 Xiaoli Han, Xishen Jin
In this paper, we give an affirmative answer to a conjecture of Collins-Yau [8]. We investigate the Chern number inequalities on 4-dimensional Kähler manifolds admitting the deformed Hermitian-Yang-Mills metrics under the assumption \({{\hat{\theta }}}\in (\pi ,2\pi )\).
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Mass-growth of triangulated auto-equivalences manuscripta math. (IF 0.6) Pub Date : 2024-01-18 Jon Woolf
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The string topology coproduct on complex and quaternionic projective space manuscripta math. (IF 0.6) Pub Date : 2024-01-18 Maximilian Stegemeyer
On the free loop space of compact symmetric spaces Ziller introduced explicit cycles generating the homology of the free loop space. We use these explicit cycles to compute the string topology coproduct on complex and quaternionic projective space. The behavior of the Goresky-Hingston product for these spaces then follows directly.
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Weak Akizuki–Nakano vanishing theorem for singular globally F-split 3-folds manuscripta math. (IF 0.6) Pub Date : 2024-01-10 Kenta Sato, Shunsuke Takagi
In this paper, we prove that a weak form of the Akizuki–Nakano vanishing theorem holds on singular globally F-split 3-folds. Making use of this vanishing theorem, we study deformations of globally F-split Fano 3-folds and the Kodaira vanishing theorem for thickenings of locally complete intersection globally F-regular 3-folds.
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Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on Del Pezzo surfaces manuscripta math. (IF 0.6) Pub Date : 2024-01-09 Purnaprajna Bangere, Jayan Mukherjee, Debaditya Raychaudhury
Let \({\mathscr {E}}\) be a vector bundle on a smooth projective variety \(X\subseteq {\mathbb {P}}^N\) that is Ulrich with respect to the hyperplane section H. In this article, we study the Koszul property of \({\mathscr {E}}\), the slope-semistability of the k-th iterated syzygy bundle \({\mathscr {S}}_k({\mathscr {E}})\) for all \(k\ge 0\) and rationality of moduli spaces of slope-stable bundles
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Characterizations of Fano type varieties and projective spaces via absolute complexity manuscripta math. (IF 0.6) Pub Date : 2024-01-04 Dae-Won Lee
In this paper, we obtain several characterizations of varieties of Fano type and projective spaces via absolute complexity. Also, we show that if the absolute complexity of a given pair \((X,\Delta )\) is negative, then the pair \((X,\Delta )\) does not admit any \(-(K_X+\Delta )\)-minimal models.
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Estimates for the average scalar curvature of the Weil–Petersson metric on the moduli space $${\overline{{{\mathcal {M}}} }}_g$$ manuscripta math. (IF 0.6) Pub Date : 2023-12-10 Georg Schumacher, Stefano Trapani
We give a precise estimate for the average scalar curvature of the Weil–Petersson metric on the moduli space \({\overline{{{\mathcal {M}}} }}_g\) as \(g\rightarrow \infty \) up to the order \(1/g^2\).
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Zeta function of some Kummer Calabi-Yau 3-folds manuscripta math. (IF 0.6) Pub Date : 2023-12-07 Dominik Burek
We compute Hodge numbers and zeta function of a Kummer Calabi-Yau 3-folds introduced by M. Andreatta and J. Wiśniewski in [2] and investigated by M. Donten-Bury in [13].
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Shifting numbers of abelian varieties via bounded t-structures manuscripta math. (IF 0.6) Pub Date : 2023-11-27 Yu-Wei Fan
The shifting numbers measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category, and are analogous to Poincaré translation numbers that are widely used in dynamical systems. Motivated by this analogy, Fan–Filip raised the following question: “Do the shifting numbers define a quasimorphism on the group of autoequivalences of a triangulated category
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The Dirichlet problem for prescribed curvature equations of p-convex hypersurfaces manuscripta math. (IF 0.6) Pub Date : 2023-11-17 Weisong Dong
In this paper, we study the Dirichlet problem for p-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An interior curvature estimate is also obtained.
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Polyharmonic surfaces in 3-dimensional homogeneous spaces manuscripta math. (IF 0.6) Pub Date : 2023-11-13 S. Montaldo, C. Oniciuc, A. Ratto
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Cuspidal components of Siegel modular forms for large discrete series representations of $$\textrm{Sp}_4({\mathbb {R}})$$ manuscripta math. (IF 0.6) Pub Date : 2023-11-13 Shuji Horinaga, Hiro-aki Narita
In this paper, we consider automorphic forms on \(\textrm{Sp}_4({\mathbb {A}}_{\mathbb {Q}})\) which generate large discrete series representations of \(\textrm{Sp}_4({\mathbb {R}})\) as \((\mathfrak {sp}_4({\mathbb {R}}),K_\infty )\)-modules. We determine the cuspidal components and the structure of the space of such automorphic forms.
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On algebraic Chern classes of flat vector bundles manuscripta math. (IF 0.6) Pub Date : 2023-11-09 Adrian Langer
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Existence of self-similar Dirichlet forms on post-critically finite fractals in terms of their resistances manuscripta math. (IF 0.6) Pub Date : 2023-11-09 Guanhua Liu
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On the rationality of certain Fano threefolds manuscripta math. (IF 0.6) Pub Date : 2023-11-06 Ciro Ciliberto
In this paper we study the rationality problem for Fano threefolds \(X\subset {\mathbb P}^{p+1}\) of genus p, that are Gorenstein, with at most canonical singularities. The main results are: (1) a trigonal Fano threefold of genus p is rational as soon as \(p\geqslant 8\) (this result has already been obtained in Przyjalkowski et al. (Izv Math 69(2):365–421, 2005), but we give here an independent proof);
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Boundedness of regular del Pezzo surfaces over imperfect fields manuscripta math. (IF 0.6) Pub Date : 2023-10-30 Hiromu Tanaka
For a regular del Pezzo surface X, we prove that \(|-12K_X|\) is very ample. Furthermore, we also give an explicit upper bound for the volume \(K_X^2\) which depends only on \([k: k^p]\) for the base field k. As a consequence, we obtain the boundedness of geometrically integral regular del Pezzo surfaces.
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Formal ternary laws and Buchstaber’s 2-groups manuscripta math. (IF 0.6) Pub Date : 2023-10-30 David Coulette, Frédéric Déglise, Jean Fasel, Jens Hornbostel
We compare formal ternary laws to Buchstaber’s 2-valued formal group laws, by means of explicit functors. We also provide a few computations of formal ternary laws of low complexity degree.
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Bounds for GL $$_2$$ $$\times $$ GL $$_2$$ L-functions in the depth aspect manuscripta math. (IF 0.6) Pub Date : 2023-10-28 Qingfeng Sun
Let f and g be holomorphic or Maass cusp forms for \(\mathrm SL_2({\mathbb {Z}})\) and let \(\chi \) be a primitive Dirichlet character of prime power conductor \(R=p^{\kappa }\) with p an odd prime and \(\kappa >12\). A subconvex bound for the central values of the Rankin–Selberg L-functions \(L(s,f\otimes g \otimes \chi )\) is proved in the depth aspect $$\begin{aligned} L\left( \frac{1}{2},f\otimes
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On classic n-universal quadratic forms over dyadic local fields manuscripta math. (IF 0.6) Pub Date : 2023-10-24 Zilong He
Let n be an integer and \( n\ge 2 \). A classic integral quadratic form over local fields is called classic n-universal if it represents all n-ary classic integral quadratic forms. We determine the equivalent conditions and minimal testing sets for classic n-universal quadratic forms over dyadic local fields.
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Moduli of Lie p-algebras manuscripta math. (IF 0.6) Pub Date : 2023-10-05 Alice Bouillet
In this paper, we study moduli spaces of finite-dimensional Lie algebras with flat center, proving that the forgetful map from Lie p-algebras to Lie algebras is an affine fibration, and we point out a new case of existence of a p-mapping. Then we illustrate these results for the special case of Lie algebras of rank 3, whose moduli space we build and study over \(\mathbb {Z}\). We extend the classical
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On a microlocal version of Young’s product theorem manuscripta math. (IF 0.6) Pub Date : 2023-09-24 Claudio Dappiaggi, Paolo Rinaldi, Federico Sclavi
A key result in distribution theory is Young’s product theorem which states that the product between two Hölder distributions \(u\in \mathcal {C}^\alpha (\mathbb {R}^d)\) and \(v\in \mathcal {C}^\beta (\mathbb {R}^d)\) can be unambiguously defined if \(\alpha +\beta >0\). We revisit the problem of multiplying two Hölder distributions from the viewpoint of microlocal analysis, using techniques proper
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The global behaviors for defocusing wave equations in two dimensional exterior region manuscripta math. (IF 0.6) Pub Date : 2023-09-18 Wei Dai
We study the defocusing semilinear wave equation in \({\mathbb {R}}\times {\mathbb {R}}^2\backslash {{\mathcal {K}}}\) with the Dirichlet boundary condition, where \({{\mathcal {K}}}\) is a star-shaped obstacle with smooth boundary. We first show that the potential energy of the solution will decay appropriately. Based on it, we show that the solution also pointwisely decays to 0. Finally, we show
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Le Laplacien conforme sur les 2-tenseurs symétriques manuscripta math. (IF 0.6) Pub Date : 2023-09-13 Erwann Delay
On any riemannian manifolds, we explicit the conformally covariant Laplacian, acting on all (fields of) covariant symmetric tensor of order two. The latter being so far expressed only on Einstein manifold and acting simply on 2-tensors without trace and with zero divergence (TT-tensors).
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Non-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension manuscripta math. (IF 0.6) Pub Date : 2023-09-05 Angelo Felice Lopez, Roberto Muñoz, José Carlos Sierra
On any smooth n-dimensional variety we give a pretty precise picture of rank r Ulrich vector bundles with numerical dimension at most \(\frac{n}{2}+r-1\). Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo fourfold of degree 6.
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On some rigidity theorems of Q-curvature manuscripta math. (IF 0.6) Pub Date : 2023-08-28 Yiyan Xu, Shihong Zhang
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A motivic interpretation of Whittaker periods for $$\textrm{GL}_n$$ manuscripta math. (IF 0.6) Pub Date : 2023-08-29 Takashi Hara, Kenichi Namikawa
Admitting the existence of conjectural motives attached to cohomological irreducible cuspidal automorphic representations of \(\textrm{GL}_n\), we write down Raghuram and Shahidi’s Whittaker periods in terms of Yoshida’s fundamental periods when the base field is a totally real number field or a CM field.
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Einstein-like metrics on compact homogeneous spaces manuscripta math. (IF 0.6) Pub Date : 2023-08-27 Feng Li, Huibin Chen, Zhiqi Chen
In this paper, we study Einstein-like metrics on compact homogeneous spaces G/H. In the beginning, we give a characterization of Einstein-like metrics on compact homogeneous spaces. As an application, we classify all invariant Einstein-like metrics on compact homogeneous spaces with two isotropy summands and generalized Wallach spaces of exceptional type.
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Weighted isoperimetric problem for spacelike hypersurface in de Sitter space manuscripta math. (IF 0.6) Pub Date : 2023-08-23 Kuicheng Ma
In this paper, we obtain the long-time existence and convergence results for a locally constrained mean curvature flow, which is nicely suitable for weighted isoperimetric problem. Using the maximum principle for tensors developed by Andrews, we show the preservation of some pinching condition along the considered flow and as an application we established the weighted isoperimetric inequality for pinched
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Stable Ulrich bundles on cubic fourfolds manuscripta math. (IF 0.6) Pub Date : 2023-08-23 Truong Le Hoang, Yen Ngoc Hoang
In this paper, we examine the presence of Ulrich bundles on cubic fourfolds. We establish necessary and sufficient conditions for the existence of Ulrich bundles of a specific rank r. As a consequence, we show the existence of a family of non-decomposable Ulrich bundles of rank r on certain cubic fourfolds, which are dependent on approximately r parameters and have wild representation type. Our study
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ACC of PLC threshold manuscripta math. (IF 0.6) Pub Date : 2023-08-22 Sung Rak Choi, Sungwook Jang
In this paper, we define the potential log canonical threshold and prove the ascending chain condition of the set of these thresholds satisfies. We also consider collections of Fano type varieties and study their basic properties including boundedness.
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On Riemannian polyhedra with non-obtuse dihedral angles in 3-manifolds with positive scalar curvature manuscripta math. (IF 0.6) Pub Date : 2023-08-22 Li Yu
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On the regularity and existence of weak solutions for a class of degenerate singular elliptic problem manuscripta math. (IF 0.6) Pub Date : 2023-08-19 Prashanta Garain
In this article, we consider a class of degenerate singular problems. The degeneracy is captured by the presence of a class of p-admissible weights, which may vanish or blow up near the origin. Further, the singularity is allowed to vary inside the domain. We provide sufficient conditions on the weight function, on the singular exponent and the source function to establish regularity and existence
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The 3-dimensional Lyness map and a self-mirror log Calabi–Yau 3-fold manuscripta math. (IF 0.6) Pub Date : 2023-08-03 Tom Ducat
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Integral points on symmetric affine cubic surfaces manuscripta math. (IF 0.6) Pub Date : 2023-08-02 H. Uppal
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A general framework for tropical differential equations manuscripta math. (IF 0.6) Pub Date : 2023-07-27 Jeffrey Giansiracusa, Stefano Mereta
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Almost complex parallelizable manifolds: Kodaira dimension and special structures manuscripta math. (IF 0.6) Pub Date : 2023-07-20 Andrea Cattaneo, Antonella Nannicini, Adriano Tomassini
We study the Kodaira dimension of a real parallelizable manifold M, with an almost complex structure J in standard form with respect to a given parallelism. For \(X = (M, J)\) we give conditions under which \({{\,\textrm{kod}\,}}(X) = 0\). We provide examples in the case \(M = G \times G\), where G is a compact connected real Lie group. Finally we describe geometrical properties of real parallelizable
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Equivariant Grothendieck ring of a complete symmetric variety of minimal rank manuscripta math. (IF 0.6) Pub Date : 2023-07-15 V. Uma
We describe the G-equivariant Grothendieck ring of a regular compactification X of an adjoint symmetric space G/H of minimal rank. This extends the results of Brion and Joshua for the equivariant Chow ring of wonderful symmetric varieties of minimal rank in (Brion, M., Joshua, R. 13, 471–493 (2008)) and generalizes the results on the regular compactification of an adjoint semisimple group in (Uma,
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Proof of Vogan’s conjecture on Arthur packets: irreducible parameters of p-adic general linear groups manuscripta math. (IF 0.6) Pub Date : 2023-07-14 Clifton Cunningham, Mishty Ray
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An arithmetic valuative criterion for proper maps of tame algebraic stacks manuscripta math. (IF 0.6) Pub Date : 2023-07-03 Giulio Bresciani, Angelo Vistoli
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Categorification of Harder–Narasimhan theory via slope functions valued in totally ordered sets manuscripta math. (IF 0.6) Pub Date : 2023-06-22 Yao Li
We introduce a categorical construction of Harder–Narasimhan filtration via a slope method which does not need a degree function. With a theorem of existence and uniqueness of Harder–Narasimhan filtration in our categorical setting, we give a categorical interpretation of Stuhler–Grayson filtration in the case of not necessarily Hermitian normed lattices.
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Max noether theorem for singular curves manuscripta math. (IF 0.6) Pub Date : 2023-06-20 Renato Vidal Martins, Edson Martins Gagliardi
Max Noether’s Theorem asserts that if \(\omega \) is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve, then the natural morphisms \(\text {Sym}^nH^0(\omega )\rightarrow H^0(\omega ^n)\) are surjective for all \(n\ge 1\). The result was extended for Gorenstein curves by many different authors in distinct ways. More recently, it was proved for curves with projectively normal canonical
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Around the motivic monodromy conjecture for non-degenerate hypersurfaces manuscripta math. (IF 0.6) Pub Date : 2023-06-19 Ming Hao Quek
We provide a new, geometric proof of the motivic monodromy conjecture for non-degenerate hypersurfaces in dimension 3, which has been proven previously by the work of Lemahieu–Van Proeyen and Bories–Veys. More generally, given a non-degenerate complex polynomial f in any number of variables and a set \(\mathbb {B}\) of \(B_1\)-facets of the Newton polyhedron of f with consistent base directions, we
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Descent study of the Lie algebra of derivations of certain infinite-dimensional Lie algebras manuscripta math. (IF 0.6) Pub Date : 2023-06-16 Hongyan Guo, Jochen Kuttler, Arturo Pianzola
Let \({\mathfrak {g}}\) be a finite-dimensional perfect Lie algebra over a field k of characteristic 0. In infinite-dimensional Lie theory we encounter Lie algebras of the form \({\mathfrak {g}}\otimes _k R\), where R is a k-ring (usually a Laurent polynomial ring in finitely many variables over k), and étale twisted forms \({\mathcal {L}}\) of \({\mathfrak {g}}\otimes _k R\). Thus \({\mathcal {L}}\)
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Bounding the signed count of real bitangents to plane quartics manuscripta math. (IF 0.6) Pub Date : 2023-06-14 Mario Kummer, Stephen McKean
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On some simple geometric structure of affine Deligne–Lusztig varieties for $${{\,\textrm{GL}\,}}_n$$ manuscripta math. (IF 0.6) Pub Date : 2023-06-12 Ryosuke Shimada
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On Frobenius stratification of moduli spaces of rank 4 vector bundles manuscripta math. (IF 0.6) Pub Date : 2023-06-12 Lingguang Li, Hongyi Zhang
Let k be an algebraically closed field of characteristic 2, X a smooth projective curve of genus \(g = 2\) over k, \(\mathcal {M}_X^s(r,d)\) the moduli space of stable vector bundles of rank r and degree d on X. We classify the Frobenius destabilized stable vector bundles of \(\textrm{rank}\ 4 \) and \( \textrm{degree}\ d\) on X in terms of the Harder-Narasimhan Polygons and study the geometry of the
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On Néron–Severi lattices of Jacobian elliptic K3 surfaces manuscripta math. (IF 0.6) Pub Date : 2023-06-04 Adrian Clingher, Andreas Malmendier
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Simplicial Chern–Weil theory for coherent analytic sheaves, part II manuscripta math. (IF 0.6) Pub Date : 2023-05-18 Timothy Hosgood
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On Lie algebra modules which are modules over semisimple group schemes manuscripta math. (IF 0.6) Pub Date : 2023-05-18 Micah Loverro, Adrian Vasiu
Let p be a prime. Given a split semisimple group scheme G over a normal integral domain R which is a faithfully flat \({\mathbb {Z}}_{(p)}\)-algebra, we classify all finite dimensional representations V of the fiber \(G_K\) of G over \(K:=Frac (R)\) with the property that the set of lattices of V with respect to R which are G-modules is as well the set of lattices of V with respect to R which are \(Lie