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2018-09

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cc-by-nc-nd (c) Elsevier B.V., 2018
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/143342

Hyperelliptic Jacobians and isogenies

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Recurs relacionat

https://doi.org/10.1016/j.aim.2018.07.025

Resum

In this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians. In the first part we prove that a very general hyperelliptic Jacobian of genus is not isogenous to a non-hyperelliptic Jacobian. As a consequence we obtain that the intermediate Jacobian of a very general cubic threefold is not isogenous to a Jacobian. Another corollary tells that the Jacobian of a very general d-gonal curve of genus is not isogenous to a different Jacobian. In the second part we consider a closed subvariety of the moduli space of principally polarized varieties of dimension . We show that if a very general element of is dominated by the Jacobian of a curve C and , then C is not hyperelliptic. In particular, if the general element in is simple, its Kummer variety does not contain rational curves. Finally we show that a closed subvariety of dimension such that the Jacobian of a very general element of is dominated by a hyperelliptic Jacobian is contained either in the hyperelliptic or in the trigonal locus.

Matèries

Matrius (Matemàtica), Geometria algebraica

Matèries (anglès)

Matrices, Algebraic geometry

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citació

NARANJO DEL VAL, Juan Carlos and PIROLA, Gian Pietro. Hyperelliptic Jacobians and isogenies. Advances in Mathematics. 2018. Vol. 335, num. 896-909. ISSN 0001-8708. [consulted: 21 of May of 2026]. Available at: https://hdl.handle.net/2445/143342

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