The geometry of the ball quotient model of the moduli space of genus four curves

Details The geometry of the ball quotient model of the moduli space of genus four curves The geometry of the ball quotient model of the moduli space of genus four curves

2011-09-26

arxiv.org/abs/1109.5669v2

Contemp. Math. 564 (2012), 107-136

Mathematics

Algebraic Geometry

in "Compact Moduli Spaces and Vector Bundles" (Proceedings of the international conference held at U. Georgia, Athens, GA, Oct

Scientific paper

S. Kondo has constructed a ball quotient compactification for the moduli space of non-hyperelliptic genus four curves. In this paper, we show that this space essentially coincides with a GIT quotient of the Chow variety of canonically embedded genus four curves. More specifically, we give an explicit description of this GIT quotient, and show that the birational map from this space to Kondo's space is resolved by the blow-up of a single point. This provides a modular interpretation of the points in the boundary of Kondo's space. Connections with the slope nine space in the Hassett-Keel program are also discussed.

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