阿贝尔微分模空间的Chern类和欧拉特征

IF 2.8 1区数学 Q1 MATHEMATICS

Forum of Mathematics Pi Pub Date : 2020-06-23 DOI:10.1017/fmp.2022.10

Matteo Costantini, Martin Möller, Jonathan Zachhuber

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引用次数: 22

摘要

摘要对于阿贝尔微分的模空间，欧拉特征是其最固有的拓扑不变量之一。给出了一个基于多尺度微分光滑紧化的交理论的欧拉特征表达式。它是紧化余切束的满陈氏多项式的一个公式的结果。主要的新技术工具是多尺度微分模空间的余切束的欧拉序列和周环中的计算工具，如将法向束描述为边界除数。

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The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials

Abstract For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth compactification by multi-scale differentials. It is a consequence of a formula for the full Chern polynomial of the cotangent bundle of the compactification. The main new technical tools are an Euler sequence for the cotangent bundle of the moduli space of multi-scale differentials and computational tools in the Chow ring, such as a description of normal bundles to boundary divisors.

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来源期刊

Forum of Mathematics Pi Mathematics-Statistics and Probability

CiteScore

3.50

自引率

0.00%

发文量

审稿时长

19 weeks

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