Modul: MAT770 Oberseminar: Algebraische Geometrie

## Abelian surfaces and orbital degeneracy loci

Prof. Dr. Laurent Manivel talk

Speaker invited by: Prof. Dr. Christian Okonek

**Date:** 01.04.19 **Time:** 13.15 - 14.45 **Room:** Y27H25

Consider an abelian surface, embedded in P^8 by its third-order theta functions. A classical observation due to Coble is that there exists a unique cubic hypersurface which is singular exactly along the surface. This result was recently revisited by Gruson, Sam and Weyman starting from a skew-symmetric three-form in nine variables. I will explain how to reconstruct, from this point of view, the generalized Kummer fourfold of the abelian surface, which is an interesting example of hyper-Kähler variety. This will allow to construct geometrically the group structure of the surface.