The p-rank stratification of Artin-Schreier curves
Rachel Pries, Hui June Zhu
Abstract
We study a moduli space ASg for Artin-Schreier curves of genus g over an algebraically closed field k of characteristic p. We study the stratification of ASg by p-rank into strata ASg,s of Artin-Schreier curves of genus g with p-rank exactly s. We enumerate the irreducible components of ASg,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 ASg is irreducible. Finally, we study deformations of Artin-Schreier curves with varying p-rank. Keywords: Artin-Schreier, hyperelliptic, curve, moduli, p-rank.
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