The \(p\)-rank stratification of Artin-Schreier curves
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Publication:441316
DOI10.5802/AIF.2692zbMATH Open1281.11062arXivmath/0609657OpenAlexW1480261356MaRDI QIDQ441316
Author name not available (Why is that?)
Publication date: 22 August 2012
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/math/0609657
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