Seminar for Algebra

On Tuesday, April 18, 2023, 15:00 hours, Emanuele Macri, Université Paris-Saclay, will hold lecture as part of Seminar for Algebra titled:

“Hyper-Kähler manifolds and Lagrangian fibrations”.

Lecture will be held in lecture room A101, Department of Mathematics.

All Seminar members and others interested are invited.

Abstract:

A hyper-Kähler manifold is a complex Kähler manifold that is simply connected, compact, and has a unique holomorphic symplectic form, up to constants. This important class of manifolds has been studied in the past in many contexts, from an arithmetic, algebraic, geometric point of view, and in applications to physics and dynamics. The theory in dimension two, namely K3 surfaces, is well understood.
The aim of the seminar is to give an introduction to the theory of hyper-Kähler manifolds in higher dimension, from a point of view of their classification; in particular, about the existence of Lagrangian fibrations.
We will present some results in dimension four, obtained recently in collaboration with Olivier Debarre, Daniel Huybrechts and Claire Voisin.