Annalisa Grossi (Université Paris-Saclay)

Abstract: Hyperkähler manifolds are one of the building blocks of compact complex Kähler manifolds with trivial first Chern class. Huybrechts proved that if X and Y are birational HK then they have to be deformation equivalent, but this implication is far from being an equivalence. It is then natural to ask which additional assumptions are needed to get that two HK manifolds of the same deformation type are birational. In this talk I will give a gentle introduction on HK manifolds and lattice theory for HK manifolds, then I will provide a lattice-theoretic criterion to determine when two HK manifolds of OG10 type are birational (joint work with C.Felisetti and F.Giovenzana), and I will show an application to the Li-Pertusi-Zhao variety. If time permits I will discuss another related topic about understanding sufficient numerical conditions to determine the deformation type of a given HK manifolds of a fixed dimension. This is a first result about a joint work in progress with P.Beri.