Algebraic Geometry Seminar

I will discuss several aspects of the geometry intermediate Jacobian fibration associated to a cubic fourfold X. This is a compact hyper-Kahler manifold with a Lagrangian fibration whose general fiber is the intermediate Jacobian of a smooth hyperplane section of X. The geometry of this hyper-Kahler manifold is governed by that of X. For example, I will show that the Mordell-Weil group of the Lagrangian fibration can be identified with the degree 4 primitive algebraic
cohomology classes on X. Speaker(s): Giulia Saccà (Columbia University)