Stability of genus five canonical curves

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.

various misprints corrected in this version. 30 pages, to appear in the proceedings of the 2011 conference in honor of Joe Harris' 60th birthday

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Cited by in corpus (1)

• Mori's program for ${\bar{M}}_{0,6}$ with symmetric divisors