Mather classes and conormal spaces of Schubert varieties in cominuscule spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-06-08 DOI:10.14231/ag-2023-019

L. Mihalcea, R. Singh

引用次数: 8

Abstract

Let $G/P$ be a complex cominuscule flag manifold. We prove a type independent formula for the torus equivariant Mather class of a Schubert variety in $G/P$, and for a Schubert variety pulled back via the natural projection $G/Q \to G/P$. We apply this to find formulae for the local Euler obstructions of Schubert varieties, and for the torus equivariant localizations of the conormal spaces of these Schubert varieties. We conjecture positivity properties for the local Euler obstructions and for the Schubert expansion of Mather classes. We check the conjectures in many cases, by utilizing results of Boe and Fu about the characteristic cycles of the intersection homology sheaves of Schubert varieties. We also conjecture that certain `Mather polynomials' are unimodal in general Lie type, and log concave in type A.

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组合空间中舒伯特变种的Mather类与共形空间

设$G/P$是一个复杂的组合标志流形。我们证明了$G/P$中Schubert变种的环面等变Mather类的一个类型无关公式，以及通过自然投影$G/Q\to G/P$拉回的Schubert变种。我们应用它来寻找Schubert变种的局部Euler阻塞的公式，以及这些Schubert变种共形空间的环面等变局部化的公式。我们猜想局部Euler阻塞和Mather类的Schubert展开的正性。利用Boe和Fu关于Schubert变种的交同调簇的特征环的结果，我们在许多情况下检验了这些猜想。我们还猜想某些“Mather多项式”在一般李型中是单峰的，在A型中是对数凹的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.