| Let X be a curve of genus 2. We denote by SUX (3) the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over X, and by Jd the variety of line bundles of degree d on X. In particular, J1 has a canonical theta divisor theta. The space SUX (3) is a double cover of P8 = |3theta| branched along a sextic hypersurface, the Coble sextic. In the dual P&d9;8 = |3theta|*, where J1 is embedded, there is a unique cubic hypersurface singular along J 1(X), the Coble cubic. We prove that these two hypersurfaces are dual, inducing a non-abelian Torelli result. Moreover, by looking at some special linear sections of these hypersurfaces, we can observe and reinterpret some classical results of algebraic geometry in a context of vector bundles: the duality of the Segre-Igusa quartic with the Segre cubic, the symmetric configuration of 15 lines and 15 points, the Weddle quartic surface and the Kummer surface. |
