Margherita Lelli Chiesa (Roma Tre): Prym-Gauss maps and curves on Abelian surfaces
Abstract: Wahl’s conjecture, finally proved by Arbarello, Bruno and Sernesi, predicted that Brill-Noether general curves lying on K3 surfaces are characterized by the non-surjectivity of their Gaussian map. Wahl himself had related the conjecture to the deformation theory of the affine cone over a canonical curve C in P^g, thus reducing part of it to the vanishing of the higher cohomology groups of the square of the ideal of C twisted by hypersurfaces of degree k>=3. I will show that the Prym-Gauss map of a Prym curve on an abelian surface is never surjective. I will then talk about a joint work in progress with Arbarello and Bruno aimed to show that a general Prym canonical curve with non-surjective Prym-Gauss map always lies on a surface in P^{g-2}. Since there is no affine cone entering this picture, during the seminar I will provide an alternative proof of Wahl’s result avoiding the deformation theory of cones.
More details can be found on https://www.imperial.ac.uk/geometry/seminars/magic-seminar/