Trigonal deformations of rank one and Jacobians
Algebraic Geometry
2018-12-24 v1
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.
Keywords
Cite
@article{arxiv.1812.09248,
title = {Trigonal deformations of rank one and Jacobians},
author = {Valentina Beorchia and Gian Pietro Pirola and Francesco Zucconi},
journal= {arXiv preprint arXiv:1812.09248},
year = {2018}
}
Comments
10 pages