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arXiv · 1203.5014

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

Sebastian Casalaina-Martin·David Jensen·Radu Laza
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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.

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Sebastian Casalaina-Martin, David Jensen, Radu Laza. 2013-02-07. Log canonical models and variation of GIT for genus four canonical curves. https://arxiv.org/abs/1203.5014

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