%0 Journal Article
%T The moduli space of rank-3 vector bundles with trivial determinant over a curve of genus 2 and duality
%A Quang Minh Nguyen
%J Mathematics
%D 2004
%I arXiv
%X Let SU_X(3) be the moduli space of semi-stable vector bundles of rank 3 and trivial determinant on a curve X of genus 2. It maps onto P^8 and the map is a double cover branched over a sextic hypersurface called the Coble sextic. In the dual P^8 there is a unique cubic hypersurface, the Coble cubic, singular exactly along the abelian surface of degree 1 line bundles on X. We give a new proof that these two hypersurfaces are dual. As an immediate corollary, we derive a Torelli-type result.
%U http://arxiv.org/abs/math/0408318v2