The Torelli locus and Newton polygons
Algebraic Geometry
2025-09-03 v1 Number Theory
Abstract
This manuscript is about abelian varieties that are Jacobians of curves. I started writing it for a lecture series at the Arizona Winter School in 2024 on abelian varieties. A longer more descriptive title might be: The Torelli locus in the moduli space of abelian varieties, with applications to Newton polygons of curves in positive characteristic. To elaborate, this manuscript covers two topics: the first is about the geometry of the Torelli locus; the second is about the arithmetic invariants of abelian varieties that occur for Jacobians of smooth curves in positive characteristic.
Cite
@article{arxiv.2509.00998,
title = {The Torelli locus and Newton polygons},
author = {Rachel Pries},
journal= {arXiv preprint arXiv:2509.00998},
year = {2025}
}
Comments
Submitted to AMS Mathematical Surveys and Monographs. Abelian Varieties: Lectures from the Arizona Winter School 2024