Log canonical models and variation of GIT for genus four canonical curves

Abstract

We discuss GIT for canonically embedded genus four curves and the connection to the Hassett-Keel program. A canonical genus four curve is a complete intersection of a quadric and a cubic, and, in contrast to the genus three case, there is a family of GIT quotients that depend on a choice of linearization. We discuss the corresponding VGIT problem and show that the resulting spaces give the final steps in the Hassett-Keel program for genus four curves.

31 pages, to appear in J. Algebraic Geom

References in corpus (6)

• Log minimal model program for the moduli space of stable curves: The first flip
• Alternate Compactifications of Moduli Spaces of Curves
• Finite Hilbert stability of (bi)canonical curves
• Singularities with G_m-action and the log minimal model program for ${\bar{M}}_g$
• GIT Constructions of Log Canonical Models of M_g
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Cited by in corpus (4)

• Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
• Log minimal model program for the moduli space of stable curves: The second flip
• Stability of genus five canonical curves
• On the birational geometry of the parameter space for codimension 2 complete intersections