The locus of curves with prescribed automorphism group

Details The locus of curves with prescribed automorphism group The locus of curves with prescribed automorphism group

2002-05-30

arxiv.org/abs/math/0205314v1

RIMS, Kyoto Technical Report Series, Communications on Arithmetic Fundamential Groups and Galois Theory, edited by H. Nakamura

Mathematics

Algebraic Geometry

21 pages, RIMS series, Kyoto University

Scientific paper

Let G be a finite group, and $g \geq 2$. We study the locus of genus g curves that admit a G-action of given type, and inclusions between such loci. We use this to study the locus of genus g curves with prescribed automorphism group G. We completely classify these loci for g=3 (including equations for the corresponding curves), and for $g \leq 10$ we classify those loci corresponding to "large" G.

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