Equations of Riemann surfaces with automorphisms

2016/07/16 by Swinarski, David
#14H37 #14H45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.04778

Abstract

We present an algorithm for computing equations of canonically embedded Riemann surfaces with automorphisms. A variant of this algorithm with many heuristic improvements is used to produce equations of Riemann surfaces X with large automorphism groups (that is, |Aut(X)| > 4(g_X-1)) for genus 4 ≤ g_X ≤ 7. The main tools are the Eichler trace formula for the character of the action of Aut(X) on holomorphic differentials, algorithms for producing matrix generators of a representation of a finite group with a specified irreducible character, and Gröbner basis techniques for computing flattening stratifications.

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