Yulieth Katterin Prieto Montañez (Università di Bologna)
Hyperkähler manifolds of K3[n]-type admitting symplectic birational maps
Motivated by the existence of birational involutions on projective hyperkähler manifolds which are deformation equivalent to Hilbert schemes of n points of K3 surfaces, we show that such hyperkähler manifolds are always birational to moduli spaces of (twisted) stable coherent sheaves on a K3 surface, when they admit a symplectic birational map of finite order with a non-trivial action on its discriminant group. Passing via Bridgeland stability, one can show these hyper- kähler manifolds are itself moduli spaces of stable objects on a (possible different) K3 surface. In the second part of this talk, we deduce properties regarding the existence of birational involutions via wall-crossing and the birational geometry of these moduli spaces. This is a work in progress with Yajnaseni Dutta and Dominique Mattei.
Wednesday, 02.03.2022, 14:00-15:00, room B302 in the main building of Leibniz Universität Hannover
