English

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 33 and any characteristic not 22: the configuration of the odd theta characteristics of a curve CC of genus 33 determines a del Pezzo surface SS of degree two and that CC is recovered as the normalization of a certain curve on SS. This surface is not the one usually associated to CC; 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.

Keywords

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}
}
R2 v1 2026-06-23T00:46:39.673Z