论文标题
感谢您的Kato歧管
Toric Kato manifolds
论文作者
论文摘要
我们介绍并研究了一类特殊的加藤歧管，我们称之为“感谢您的Kato歧管”。它们的构造源于复曲面的几何形状，因为它们的通用覆盖物是非有限类型的感谢您的代数变种的开放子集。这概括了Tsuchihashi和Oda的先前结构，并且在复杂的维度2中检索了正确吹动的Inoue表面。我们研究了感谢您的Kato歧管的拓扑和分析特性，并将某些不变性链接到来自复曲面结构的自然组合数据。此外，我们产生了任何复金托歧管的平坦变性的家族，它们是计算其霍奇数字的必不可少的工具。在最后一部分中，我们研究了加藤歧管的隐居几何形状。我们给出了在任何Kato歧管上存在局部合成的Kähler指标的表征结果。最后，我们证明，没有加利福尼亚的歧管均具有平衡的指标，并且一大批复杂尺寸的感谢您的Kato歧管$ \ geq 3 $不支持多lic液指标。
We introduce and study a special class of Kato manifolds, which we call toric Kato manifolds. Their construction stems from toric geometry, as their universal covers are open subsets of toric algebraic varieties of non-finite type. This generalizes previous constructions of Tsuchihashi and Oda, and in complex dimension 2, retrieves the properly blown-up Inoue surfaces. We study the topological and analytical properties of toric Kato manifolds and link certain invariants to natural combinatorial data coming from the toric construction. Moreover, we produce families of flat degenerations of any toric Kato manifold, which serve as an essential tool in computing their Hodge numbers. In the last part, we study the Hermitian geometry of Kato manifolds. We give a characterization result for the existence of locally conformally Kähler metrics on any Kato manifold. Finally, we prove that no Kato manifold carries balanced metrics and that a large class of toric Kato manifolds of complex dimension $\geq 3$ do not support pluriclosed metrics.
