小平维度与山边问题 II

Pub Date : 2024-07-29 DOI:10.4310/cag.2023.v31.n10.a4

Albanese,Michael, LeBrun,Claude

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引用次数: 0

摘要

对于凯勒类型的紧凑复曲面$(M^{4}, J)$，之前已经证明[30]山边不变量$m\mathscr{Y}(M)$的符号只取决于柯达伊拉维度$\text{Kod} (M, J)$。在本文中，我们证明了这一模式事实上扩展到了除第 VII 类之外的所有紧凑复曲面。在此过程中，我们还重新证明了[2]中的一个结果，它解释了为什么这里必须排除第 VII 类。

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Kodaira dimension & the Yamabe problem, II

For compact complex surfaces $(M^{4}, J)$ of Kähler type, it was previously shown [30] that the sign of the Yamabe invariant $\mathscr{Y}(M)$ only depends on the Kodaira dimension $\text{Kod} (M, J)$. In this paper, we prove that this pattern in fact extends to all compact complex surfaces except those of class VII. In the process, we also reprove a result from [2] that explains why the exclusion of class VII is essential here.

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