复维度六的不可约紧超凯勒流形第二贝蒂数的一个上界
微分几何
2021-12-28 v2 代数几何
摘要
设 M 为复维度六的不可约紧超凯勒流形。在对 M 的上同调的 Looijenga-Lunts-Verbitsky 分解作一假设下，我们证明 M 的第二贝蒂数至多为 23。
引用
@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}
}
备注
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)