Tropes, Torelli and theta characteristics
Algebraic Geometry
2019-12-10 v2
Abstract
Our main result is an effective version of the Torelli theorem in genus and any characteristic not : the configuration of the odd theta characteristics of a curve of genus determines a del Pezzo surface of degree two and that is recovered as the normalization of a certain curve on . This surface is not the one usually associated to ; we describe the distinction. We also give an explicit geometrical description of the quadratic twist (observed by Serre) that arises in the statement of the Torelli theorem.
Cite
@article{arxiv.1803.03138,
title = {Tropes, Torelli and theta characteristics},
author = {M. J. Fryers and N. I. Shepherd-Barron},
journal= {arXiv preprint arXiv:1803.03138},
year = {2019}
}