上同调交数的局部化公式

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Mathematical Society of Japan Pub Date : 2021-04-26 DOI:10.2969/jmsj/87738773

Saiei-Jaeyeong Matsubara-Heo

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引用次数: 3

摘要

我们重新讨论了与对数连接相关的上同调交集的局部化公式。本文的主要贡献有三个方面：我们用连接的余数证明了对数形式上同调交集的局部化公式；我们证明了当连接是超几何时，上同调交集数的Laurent展开的前导项是Grothendieck残数；证明了Arkani-Hamed、He和Lam讨论的弦积分的前导项只不过是正则形式的自上同调交数。

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Localization formulas of cohomology intersection numbers

We revisit the localization formulas of cohomology intersection numbers associated to a logarithmic connection. The main contribution of this paper is threefold: we prove the localization formula of the cohomology intersection number of logarithmic forms in terms of residue of a connection; we prove that the leading term of the Laurent expansion of the cohomology intersection number is Grothendieck residue when the connection is hypergeometric; and we prove that the leading term of stringy integral discussed by Arkani-Hamed, He and Lam is nothing but the self-cohomology intersection number of the canonical form.

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来源期刊

Journal of the Mathematical Society of Japan 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Mathematical Society of Japan (JMSJ) was founded in 1948 and is published quarterly by the Mathematical Society of Japan (MSJ). It covers a wide range of pure mathematics. To maintain high standards, research articles in the journal are selected by the editorial board with the aid of distinguished international referees. Electronic access to the articles is offered through Project Euclid and J-STAGE. We provide free access to back issues three years after publication (available also at Online Index).