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arXiv · 1812.09248

Trigonal deformations of rank one and Jacobians

Valentina Beorchia·Gian Pietro Pirola·Francesco Zucconi
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Abstract

In this paper we study the infinitesimal deformations of a trigonal curve that preserve the trigonal series and such that the associate infinitesimal variation of Hodge structure (IVHS) is of rank 1. We show that if the genus g is greater or equal to 8 or g=6,7 and the curve is Maroni general, this locus is zero dimensional. Moreover, we complete a result of Naranjo and Pirola. We show in fact that if the genus g is greater or equal to 6, the hyperelliptic locus is the only 2g-1-dimensional sub-locus Y of the moduli space of curves of genus g, such that for the general element [C] in Y, its Jacobian J(C) is dominated by a hyperelliptic Jacobian of genus g' greater or equal to g.

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Valentina Beorchia, Gian Pietro Pirola, Francesco Zucconi. 2018-12-21. Trigonal deformations of rank one and Jacobians. https://arxiv.org/abs/1812.09248

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