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

TL;DR

This paper establishes an upper bound of 23 for the second Betti number of certain six-dimensional hyperk"ahler manifolds, assuming a specific cohomological decomposition.

Contribution

It provides a new bound on the second Betti number for complex six-dimensional hyperk"ahler manifolds under a particular cohomological assumption.

Findings

Second Betti number of such manifolds is at most 23

Bound depends on an assumption about the Looijenga-Lunts-Verbitsky decomposition

Advances understanding of topological constraints in hyperk"ahler 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.