On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four

We extend a result of Guan by showing that the second Betti number of a 4-dimensional primitively symplectic orbifold is at most 23 and there are at most 91 singular points. The maximal possibility 23 can only occur in the smooth case. In addition to the known smooth examples with second Betti numbe...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Fu, Lie, Menet, Grégoire
Format: Article
Language:English
Online Access:Get full text
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Summary:We extend a result of Guan by showing that the second Betti number of a 4-dimensional primitively symplectic orbifold is at most 23 and there are at most 91 singular points. The maximal possibility 23 can only occur in the smooth case. In addition to the known smooth examples with second Betti numbers 7 and 23, we provide examples of such orbifolds with second Betti numbers 3, 5, 6, 8, 9, 10, 11, 14 and 16. In an appendix, we extend Salamon's relation among Betti/Hodge numbers of symplectic manifolds to symplectic orbifolds.
ISSN:2331-8422
DOI:10.48550/arxiv.2001.06643