On the geometry of the second fundamental form of the Torelli map
Algebraic Geometry
2020-10-13 v2
Abstract
In this paper we give a geometric interpretation of the second fundamental form of the period map of curves and we use it to improve the upper bounds on the dimension of a totally geodesic subvariety Y of A_g generically contained in the Torelli locus obtained in [3], [7]. We get dim Y < 2g if g is even, dim Y < 2g+1 if g is odd. We also study totally geodesic subvarieties Z of A_g generically contained in the hyperelliptic Torelli locus and we show that dim Z < g+2.
Keywords
Cite
@article{arxiv.1907.11407,
title = {On the geometry of the second fundamental form of the Torelli map},
author = {Paola Frediani and Gian Pietro Pirola},
journal= {arXiv preprint arXiv:1907.11407},
year = {2020}
}
Comments
Final version. To appear in Proceedings of the AMS