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arXiv · 1607.04778

Equations of Riemann surfaces with automorphisms

David Swinarski
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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, $|\mathrm{Aut}(X)| > 4(g_X-1)$) for genus $4 \leq g_X \leq 7$. The main tools are the Eichler trace formula for the character of the action of $\mathrm{Aut}(X)$ on holomorphic differentials, algorithms for producing matrix generators of a representation of a finite group with a specified irreducible character, and Gr\"obner basis techniques for computing flattening stratifications.

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David Swinarski. 2016-07-16. Equations of Riemann surfaces with automorphisms. https://arxiv.org/abs/1607.04778

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