A conjectural bound on the second betti number for Hyper-KÄhler Manifolds

Yoon Joo Kim; Radu Laza

doi:10.24033/BSMF.2813

A conjectural bound on the second betti number for Hyper-KÄhler Manifolds

Yoon Joo Kim
, Radu Laza

Mathematics

Stony Brook University

Stony Brook University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In a previous work ([1]), we noted that the known cases of hyper-Kähler 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-Kähler manifolds, we obtain an upper bound for the second Betti number in terms of the dimension.

Original language	English
Pages (from-to)	467-480
Number of pages	14
Journal	Bulletin de la Societe Mathematique de France
Volume	148
Issue number	3
DOIs	https://doi.org/10.24033/BSMF.2813
State	Published - 2020

Keywords

Hyper-Kähler manifold
Second Betti number

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10.24033/BSMF.2813

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abstract = "In a previous work ([1]), we noted that the known cases of hyper-K{\"a}hler 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{\"a}hler manifolds, we obtain an upper bound for the second Betti number in terms of the dimension.",

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KW - Hyper-Kähler manifold

KW - Second Betti number

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A conjectural bound on the second betti number for Hyper-KÄhler Manifolds

Abstract

Keywords

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