Stability of genus five canonical curves

Maksym Fedorchuk; David Ishii Smyth

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arXiv · 1302.4804

Stability of genus five canonical curves

Maksym Fedorchuk·David Ishii Smyth

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Abstract

We analyze GIT stability of nets of quadrics in $\mathbb{P}^4$ up to projective equivalence. Since a general net of quadrics defines a canonically embedded smooth curve of genus five, the resulting GIT quotient gives a birational model of the moduli space of genus 5 curves. We study the geometry of the associated contraction and prove that the constructed GIT quotient is the final step of the log minimal model program for the moduli space of genus 5 curves.

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Maksym Fedorchuk, David Ishii Smyth. 2013-02-20. Stability of genus five canonical curves. https://arxiv.org/abs/1302.4804

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