Artin-Schreier curves
Date
2010
Authors
Farnell, Shawn, author
Pries, Rachel, advisor
Achter, Jeffrey D., committee member
Peterson, Christopher Scott, 1963-, committee member
Gelfand, Martin Paul, committee member
Journal Title
Journal ISSN
Volume Title
Abstract
Let k be an algebraically closed field of characteristic p where p is a prime number. The main focus of this work is on properties of Artin-Schreier curves. In particular, we study two invariants of the p-torsion of the Jacobian of these curves: the p-rank and the a-number. In the main result, we demonstrate a family of Artin-Schreier curves for which the a-number is constant. We also give a result concerning the existence of deformations of Artin-Schreier curves with varying p-rank.
Description
Rights Access
Subject
Artin-Schreier
moduli
invariant
deformation
curve
Curves, Algebraic
Deformations of singularities
Moduli theory
Smooth affine curves
Jacobians