A bound on the second Betti number of hyperkähler manifolds of complex dimension six

Abstract

Let M be an irreducible compact hyperkähler manifold of complex dimension six. Under an assumption on the Looijenga-Lunts-Verbitsky decomposition of the cohomology of M, we prove that the second Betti number of M is at most 23.

arXiv comment13 pages, 2 figures; the proofs of Theorems 3 and 4 in v1 both require additional assumptions on the Looijenga-Lunts-Verbitsky decomposition of the cohomology of M, that we have added in v2 (thanks to Colleen Robles for pointing this out)