Families and moduli of covers with specified ramification

2013/12/26 by Ryan Eberhart, Eberhart, Ryan · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.1312.7144

Abstract

We study branched covers of curves with specified ramification points, under a notion of equivalence derived from linear series. In characteristic 0, no non-constant families of covers with fixed ramification points exist. In positive characteristic we formulate a necessary and sufficient condition for the existence of such a family. We unconditionally prove one direction of this conjecture, and by studying infinitesimal deformations show the other direction in characteristic 2 and 3.

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• Analogs of the Shapiro Shapiro Conjecture in Positive Characteristic

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