Algebraic Geometry Seminar
Giulia Sacca
Stonybrook
Intermediate Jacobians and hyperKahler manifolds
Abstract: In recent years, there have been an increasing number of connections between
cubic 4folds and hyperkahler manifolds. The aim of the talk is to
give background in this area and then describe another instance of
this phenomenon, which is carried out in
joint work with R. Laza and C. Voisin:
Given a general cubic 4fold X, one may consider the universal family
Y_U \to U of smooth hyperplanes sections of X and the relative
Intermediate Jacobian fibration f: J_U \to U. In 1995 Donagi and
Markman constructed a holomorphic symplectic form on J_U, with respect
to which the fibration f is Lagrangian. Since then, there have been
many attempts to find a smooth hyperkahler compactification of J_U.
This was conjectured to exist and to be deformation equivalent to
O'Grady's 10--dimensional exceptional example. With Radu Laza and Claire
Voisin, we solve this conjecture by using relative compactified Prym
varieties.
Wednesday November 2, 2016 at 4:00 PM in SEO 427