In search of maximal branes on compact hyper-Kähler manifolds

par Annalisa Grossi (Bologna)

jeudi 20 nov. 2025, 14:00 → 16:00 Europe/Paris

Given a holomorphic or anti-holomorphic involution on a complex manifold, the Smith-Thom inequality says that the total F2-Betti number of the fixed locus is no greater than the total F2-Betti number of the ambient manifold. The involution is called maximal when the equality is achieved. Recently it has been investigated the existence problem for maximal involutions on K3 surfaces, the unique 2-dimensional compact hyper-Kähler manifolds. A natural further question is to investigate what happens on higher-dimensional compact hyper-Kähler manifolds, where the name "maximal brane" refers to the fixed locus of a maximal involution. In this talk I will introduce hyper-Kähler manifolds and I will show a recent result with Billi, Fu and Kharlamov about the non-existence of maximal branes on hyper-Kähler manifolds of K3^[n]-type.