Abstract
We study the moduli space ASg of Artin-Schreier curves of genus g over an algebraically closed field k of positive characteristic p. The moduli space is partitioned into strata, which are irreducible. Each stratum parameterizes Artin-Schreier curves whose ramification divisors have the same coefficients. We construct deformations of these curves to study the relations between those strata. As an application, when p=3, we prove that ASg is connected for all g. When p>3, it turns out that ASg is connected for a sufficiently large value of g. In the course of our work, we answer a question of Pries and Zhu about how a combinatorial graph determines the geometry of ASg.
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