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

Author(s)

Fu, Lie ^{[1, 2]} ; Menet, Gregoire ^[3]

Affiliation

^[1] Radboud Univ Nijmegen, IMAPP, Nijmegen - Netherlands

^[2] Univ Claude Bernard Lyon 1, Inst Camille Jordan, Lyon - France

^[3] Inst Fourier, 100 Rue Math, Gieres - France

• Document type: Journal article
• Source: MATHEMATISCHE ZEITSCHRIFT; v. 299, n. 1-2, p. 203-231, OCT 2021.
• Web of Science Citations: 0

Abstract

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. (AU)

• FAPESP's process: 14/05733-9 - Geometry of irreducible symplectic varieties
• Grantee: Grégoire Menet
• Support Opportunities: Scholarships in Brazil - Post-Doctoral