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The locus of curves with prescribed automorphism group

K. Magaard·T. Shaska·S. Shpectorov·H. Voelklein
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Abstract

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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K. Magaard, T. Shaska, S. Shpectorov, H. Voelklein. 2002-05-30. The locus of curves with prescribed automorphism group. https://arxiv.org/abs/math/0205314

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