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.

中文翻译：

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关于四维紧全纯辛折线的贝蒂数

我们扩展了 Guan 的结果，证明 4 维原始辛轨道的第二个 Betti 数最多为 23，并且最多有 91 个奇异点。最大可能性 23 只能出现在光滑的情况下。除了已知的带有第二个 Betti 数 7 和 23 的平滑示例之外，我们还提供了带有第二个 Betti 数 3、5、6、8、9、10、11、14 和 16 的此类轨道的示例。在附录中，我们扩展了 Salamon 的辛流形的 Betti/Hodge 数与辛 orbifolds 之间的关系。