Ben Bakker : The Matsushita alternative

Posted by Ben Bakker , part of the Algebraic Geometry Seminar.

At

April 17, 2023, noon

In

636 SEO

Abstract

Compact hyperkahler manifolds are higher-dimensional generalizations of K3 surfaces; their geometry is tightly constrained by the existence of a holomorphic symplectic form. For example, a result of Matsushita says the only nontrivial fibration structures they admit are fibrations by Lagrangian tori. In this talk I'll explain how to prove a conjecture of Matsushita that such fibrations are either isotrivial or vary maximally in moduli. I will also discuss some other features of the topology of Lagrangian fibrations and a result about the density of torsion points in sections.