Boundness of $b_2$ for hyperkähler manifolds with vanishing odd-Betti numbers

Abstract

We prove that $b_2$ is bounded for hyperkähler manifolds with vanishing odd-Betti numbers. The explicit upper boundary is conjectured. Following the method described by Sawon we prove that $b_2$ is bounded in dimension eight and ten in the case of vanishing odd-Betti numbers by 24 and 25 respectively.

10 pages

References in corpus (1)

• A Lie algebra attached to a projective variety

Cited by in corpus (1)

• A conjectural bound on the second Betti number for hyper-Kähler manifolds