The locus of curves with prescribed automorphism group

Abstract

Let G be a finite group, and $g\ge 2$. 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 $g\le 10$ we classify those loci corresponding to "large" G.

Updated references

Cited by in corpus (21)

• Determining equations of families of cyclic curves
• From hyperelliptic to superelliptic curves
• Thetanulls of cyclic curves of small genus
• Branes through finite group actions
• Bielliptic curves of genus 3 in the hyperelliptic moduli
• The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three
• A note on large automorphism groups of compact Riemann surfaces
• On Riemann surfaces of genus $g$ with $4g-4$ automorphisms
• On isogenies among certain abelian surfaces
• Experiments with Ceresa classes of cyclic Fermat quotients
• On The Group Algebra Decomposition of a Jacobian Variety
• The case for superelliptic curves
• Branching data for curves up to genus 48
• Cyclic Automorphisms groups of genus 10 non-hyperelliptic curves
• Locus of curves with D_n-symmetry inside M_g
• Computational Aspects of Hyperelliptic Curves
• Decomposition of Jacobian varieties of curves with dihedral actions via equisymmetric stratification
• Minimal Weierstrass equations for genus 2 curves
• Superelliptic curves with minimal weighted moduli height
• Cyclic covers of Stable curves and their moduli spaces
• Automorphism groups of pseudoreal Riemann surfaces