descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 15 Sep 2016Embargo end date: 01 Jan 2014Publisher:Foundation Compositio MathematicaJournal:Algebraic Geometry, volume 3, pages 424-440 (eissn: 2214-2584,

Authors: Marcucci, Valeria; Naranjo, Juan Carlos; PIROLA, GIAN PIETRO;

doi: 10.14231/ag-2016-020 , 10.48550/arxiv.1405.2545

arXiv: http://arxiv.org/abs/1405.2545

handle: 2445/174102 , 2445/174060 , 2445/174112 , 2445/174132 , 11571/1174602

Isogenies of Jacobians

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Abstract

We prove by means of the study of the infinitesimal variation of Hodge structure and a generalization of the classical Babbage-Enriques-Petri theorem that the Jacobian variety of a generic element of a $k$ codimensional subvariety of $\mathcal M_g$ is not isogenous to a distinct Jacobian if $g>3k+4$. We extend this result to $k=1, g\ge 5$ by using degeneration methods.

Final version with minor corrections. To appear in Algebraic Geometry

Related Organizations

University of Barcelona
Spain
University of Pavia
Italy

Keywords

Equacions de Hamilton-Jacobi, Isogeny, 510, Varietats abelianes, Mathematics - Algebraic Geometry, Abelian varieties, FOS: Mathematics, Hamilton-Jacobi equations, Càlcul de variacions, Algebraic Geometry (math.AG), Jacobian, Calculus of variations

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