Algebraic Geometry Seminar
Ben Bakker
UIC
The Matsushita alternative
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.
Monday April 17, 2023 at 12:00 PM in 636 SEO