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

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

2012-03-22

arxiv.org/abs/1203.5014v1

Mathematics

Algebraic Geometry

27 pages

Scientific paper

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.

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