Birational geometry of moduli of curves with an $S_3$-cover

Abstract

We consider the space ${\mathcal{R}}_{g,S_3}^{S_3}$ of curves with a connected $S_3$-cover, proving that for any odd genus $g\ge 13$ this moduli is of general type. Furthermore we develop a set of tools that are essential in approaching the case of $G$-covers for any finite group $G$.

32 pages, 1 figure

References in corpus (4)

• Pointed Admissible G-Covers and G-equivariant Cohomological Field Theories
• Syzygies of torsion bundles and the geometry of the level l modular variety over M_g
• Tautological and non-tautological cohomology of the moduli space of curves
• Effective divisors on \bar{M}_g, curves on K3 surfaces and the Slope Conjecture