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

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

2011-06-24

arxiv.org/abs/1106.5012v2

Mathematics

Algebraic Geometry

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

Scientific paper

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 $\bar{M}_4$.

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