The locus of curves with prescribed automorphism group
Abstract
Let G be a finite group, and g ≥ 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 ≤ 10 we classify those loci corresponding to "large" G.
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