Cohomology of Hyperkaehler manifolds
-- Radu Laza, February 28, 2020
The hyperkaehler manifolds are important building blocks in algebraic geometry. They are higher dimensional analogues of K3 surfaces, in the sense that their second cohomology controls their geometry (cf. Verbitsky's Torelli theorem). In this talk, I will discuss the extent to which the second cohomology controls the higher cohomology of hyperkaher manifolds. As a consequence, I will present a conjectural bound on the second Betti numbers for hyperkahler manifolds.
This is joint with M. Green, YJ Kim, and C. Robles