戈伦斯坦法向曲面奇点的复元分类

IF 1 3区数学 Q1 MATHEMATICS

Mathematische Zeitschrift Pub Date : 2024-07-02 DOI:10.1007/s00209-024-03530-8

András Némethi, Gergő Schefler

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引用次数: 0

摘要

考虑一个复正则面奇异性及其三个复元，即渡边（Watanabe）的第m个（L^2\）复元、诺勒（Knöller）的第m个复元和莫拉莱斯（Morales）的第m个对数复元。对于这些不变式中的任何一个，我们都会构造一个双分级（\mathbb {Z}[U]\ ）模块，其欧拉特征就是所选的诸元。我们将这三个结果与胚芽的解析晶格同调进行比较，后者的欧拉特征是经典几何属。

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Categorification of the plurigenera of Gorenstein normal surface singularities

Consider a complex normal surface singularity and its three plurigenera, the m-th \(L^2\)–plurigenus of Watanabe, the m-th plurigenus of Knöller and the m-th log-plurigenus of Morales. For any of these invariants we construct a double graded \(\mathbb {Z}[U]\)–module, whose Euler characteristic is the chosen plurigenus. The three outputs are compared with the analytic lattice cohomology of the germ, whose Euler characteristic is the classical geometric genus.

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