Programm des Emmy-Noether-Seminars

Fri, 14.07.2017, 14:30

Fri, 14.07.2017, 15:30
Automorphisms of special irreducible holomorphic symplectic manifolds

Speaker: Prof. Alessandra Sarti (Poitiers)
Host: Knop
Room: 04.363

Irreducible holomorphic symplectic manifolds can be seen as a higher dimensional generalization of K3 surfaces, with which they share several interesting properties. After recalling some basic facts, I will in particular present the necessary tools for the study of their automorphisms group.
I will report on recent results in collaboration with Samuel Boissière, Andrea Cattaneo and Marc Nieper-Wisskirchen on the automorphism group of the Hilbert scheme of two points on a generic K3 surface of any polarization. In this case the Picard  number of the Hilbert scheme is two, which is the minimal possible. In particular by using ampleness results of Bayer-Macri and a detailed study of the isometries of the Picard lattice, I show the existence of non-natural non-symplectic involutions on some Hilbert scheme, depending on the degree of the polarization. In all the results the solutions of certain Pell's equation play a fundamental role.