Results 31 to 40 of about 2,842 (71)
The geometry and arithmetic of bielliptic Picard curves
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
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Parity of ranks of Jacobians of curves
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser +3 more
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Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract We show that the hyper‐Kähler varieties of OG10‐type constructed by Laza–Saccà–Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general result, stating that certain Lagrangian fibrations verify this conjecture. The main technical assumption of this general result is that the Lagrangian fibration satisfies
Giuseppe Ancona +3 more
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Families of simple Jacobians with many automorphisms
Algebraic GeometryWe study an explicit (2 g − 1)-dimensional family of Jacobian varieties of dimension 12 ( d − 1)( g − 1), arising from quotient curves of unramified cyclic coverings of prime degree d of hyperelliptic curves of genus g ⩾ 2.
J. Naranjo +3 more
semanticscholar +1 more source
Theta-duality in abelian varieties and the bicanonical map of irregular varieties
, 2010 The first goal of this Thesis is to contribute to the study of principally polarized abelian varieties (ppav), especially to the Schottky and the Torelli problems.
Martí Lahoz Vilalta
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Jacobian varieties with group algebra decomposition not affordable by Prym varieties
Journal of Pure and Applied AlgebraThe action of a finite group $G$ on a compact Riemann surface $X$ naturally induces another action of $G$ on its Jacobian variety $\operatorname{J}(X)$. In many cases, each component of the group algebra decomposition of $\operatorname{J}(X)$ is isogenous to a Prym varieties of an intermediate covering of the Galois covering $π_G\colon X \to X/G$; in ...
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Singularities of theta divisors and the Tannakian Schottky problem
Mathematische AnnalenWith the Tannakian formalism, one can attach to any principally polarized abelian variety a reductive group, along with a representation. We obtain a completely new characterization of Jacobians relying on this Tannakian data and certain characteristic ...
Constantin Podelski
semanticscholar +1 more source
Abhandlungen aus dem Mathematischen Seminar der Universität HamburgAbstract We give a description of the intermediate Jacobian fibration attached to a general complex cubic fourfold X containing a plane as a Lagrangian subfibration of a moduli space of torsion sheaves on the K3 surface associated to X up to a cover.
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Prym varieties that are not isomorphic to Jacobian
We study Prym varieties of ramified (at precisely two points) double covers of smooth irreducible complex projectives curves that admit an automorphism of prime order $p>2$. Using Galois theory, we give an explicit constructions of Prym varieties that are not isomorphic to jacobians (even if one ignores the polarizations).
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