Betti numbers of large semiprojective hyperkaehler varieties
Vortrag von Prof. Dr. Tamás Hausel
Datum: 14.10.13 Zeit: 13.30 - 15.00 Raum: Y27H25
After reviewing cohomological properties of semiprojective varieties we will discuss certain arithmetic techniques, which have been used to determine the Betti numbers of many families of semiprojective hyperkaehler manifolds. The formulas are in a combinatorial form, which makes computation of the Betti numbers for large examples feasible. We will consider limiting behaviours of the graph of Betti numbers of such large hyperkahler manifolds. We find that in various examples the Gauss, Gumbel and Airy distributions appear as the limit. This is joint work with Fernando Rodriguez Villegas.