The moduli space of rank-3 vector bundles with trivial determinant over a curve of genus 2 and duality

Abstract

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.

20 pages. v2

References in corpus (1)

• Sur l'espace des modules des fibres vectoriels de rang 3 sur une courbe de genre 2 et la cubique de Coble

Cited by in corpus (1)

• Vector bundles on curves and theta functions