The final log canonical model of the moduli space of stable curves of genus four

Abstract

We describe the final log canonical model of the moduli space of stable curves of genus four. We prove that the rational map from ${\bar{M}}_4$ to this model contracts the Petri and the boundary divisors and flips the hyperelliptic locus. As an application, we find an exact bound on slopes of moving divisors on ${\bar{M}}_4$.

18 pages, 2 figures, 1 table. To appear in Int. Math. Res. Notices

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Cited by in corpus (4)

• Effective divisors on moduli spaces of curves and abelian varieties
• GIT and moduli with a twist
• Finite Hilbert stability of canonical curves, II. The even-genus case
• Theta characteristics and their moduli