%0 Journal Article
%T Stability of genus five canonical curves
%A Maksym Fedorchuk
%A David Ishii Smyth
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1302.4804v2