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

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATISCHE ZEITSCHRIFT; v. 299, n. 1-2, p. 203-231, OCT 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/05733-9 - Geometria de variedades simpléticas irredutíveis
• Beneficiário: Grégoire Menet
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado