Leicester Pure Mathematics Seminar, 10/12/2009

MAB 119 3:30 pm   Paola Frediani (University of Pavia)

"Some results on the second Gaussian map for curves"

Abstract:

We study the second Gaussian map for a curve X of genus g, in relation

with the second fundamental form of the period map.

In fact one shows that the holomorphic sectional curvature of M_g along a Schiffer

variation at a point P on the curve X can be expressed in terms of the

holomorphic sectional curvature of A_g and the second Gaussian map.

We study the rank of the second Gaussian map, in particular when the curve is contained in a 

K3 surface or in an abelian surface. 

These results are obtained in collaboration with Elisabetta Colombo and 

Giuseppe Pareschi.