Séminaires

Coble’s classical construction provides an embedding in P8 of a genus 2 Jacobian as singular locus of a unique cubic hypersurface; similarly, the Kummer surface of a genus 3 Jacobian is embedded in P7 as the singular locus of a unique quartic hypersurface. These cubics and quartics are known as Coble hypersurfaces, and Beauville proved that their existence follows from the theory of representations of the Heisenberg group. For two 20-dimensional locally complete families of projective hyperkaehler fourfolds, one can prove the existence of « Coble type » hypersurfaces, and a similar approach to that of Beauville allows to give their explicit equation in some special cases. This talk is based on joint work (partially in progress) with Á.D. Ríos Ortiz, A. Rojas, J. Song.