English

A conjectural bound on the second Betti number for hyper-K\"ahler manifolds

Algebraic Geometry 2022-02-08 v3

Abstract

In previous work, we noted that the known cases of hyper-K\"ahler manifolds satisfy a natural condition on the LLV decomposition of the cohomology; informally, the Verbitsky component is the dominant representation in the LLV decomposition. Assuming this condition holds for all hyper-K\"ahler manifolds, we obtain an upper bound for the second Betti number in terms of the dimension.

Keywords

Cite

@article{arxiv.1909.06924,
  title  = {A conjectural bound on the second Betti number for hyper-K\"ahler manifolds},
  author = {Yoon-Joo Kim and Radu Laza},
  journal= {arXiv preprint arXiv:1909.06924},
  year   = {2022}
}

Comments

9 pages; to appear in Bull. Soc. Math. France. Final version