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https://hdl.handle.net/2445/143342
Title: | Hyperelliptic Jacobians and isogenies |
Author: | Naranjo del Val, Juan Carlos Pirola, Gian Pietro |
Keywords: | Matrius (Matemàtica) Geometria algebraica Matrices Algebraic geometry |
Issue Date: | Sep-2018 |
Publisher: | Elsevier B.V. |
Abstract: | 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.aim.2018.07.025 |
It is part of: | Advances in Mathematics, 2018, vol. 335, p. 896-909 |
URI: | https://hdl.handle.net/2445/143342 |
Related resource: | https://doi.org/10.1016/j.aim.2018.07.025 |
ISSN: | 0001-8708 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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