Betti numbers of hyperkahler manifolds


In this talk i will introduce known results on Beauville conjecture. In particular, i will explain boundary conditions for the second Betti number which follows from Rozansky-Witten invariants and so(4, b_2-2)-action on cohomology. Guan has proved that in dimension four there can exist only finite numbers of hyperkahler manifolds. In dimension six and more some results are obtained by Sawon and Kurnosov.