English

A bound on the second Betti number of hyperk\"ahler manifolds of complex dimension six

Differential Geometry 2021-12-28 v2 Algebraic Geometry

Abstract

Let M be an irreducible compact hyperk\"ahler 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.

Keywords

Cite

@article{arxiv.1511.09105,
  title  = {A bound on the second Betti number of hyperk\"ahler manifolds of complex dimension six},
  author = {Justin Sawon},
  journal= {arXiv preprint arXiv:1511.09105},
  year   = {2021}
}

Comments

13 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)