The p-rank stratification of Artin-Schreier curves
Number Theory
2016-01-15 v3 Algebraic Geometry
Abstract
We study a moduli space AS_g for Artin-Schreier curves of genus g over an algebraically closed field k of characteristic p. We study the stratification of AS_g by p-rank into strata AS_{g,s} of Artin-Schreier curves of genus g with p-rank exactly s. We enumerate the irreducible components of AS_{g,s} and find their dimensions. As an application, when p=2, we prove that every irreducible component of the moduli space of hyperelliptic k-curves with genus g and 2-rank s has dimension g-1+s. We also determine all pairs (p,g) for which AS_g is irreducible. Finally, we study deformations of Artin-Schreier curves with varying p-rank. Keywords: Artin-Schreier, hyperelliptic, curve, moduli, p-rank.
Keywords
Cite
@article{arxiv.math/0609657,
title = {The p-rank stratification of Artin-Schreier curves},
author = {Rachel Pries and Hui June Zhu},
journal= {arXiv preprint arXiv:math/0609657},
year = {2016}
}
Comments
Revisions made in Section 3 and new result added