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