希钦断裂的一个支持定理:以GLn和KC为例

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-09-03 DOI:10.1515/crelle-2021-0045

M. A. D. de Cataldo, J. Heinloth, L. Migliorini

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引用次数: 2

摘要

摘要本文计算了GLn {\mathrm{GL} ＿n{在简化谱曲线轨迹上的Hitchin振动反常上同轴的支点。与亚纯希格斯场相比，我们在可约谱曲线的轨迹处发现了额外的支撑。它们对全局上同调的贡献是由李维子群的希钦纤曲的有限扭曲所支配的。相应的和对每个n≥}}2n{的模空间的上同调给出了非平凡的贡献\geq{2}}。一个关键的因素是交叉上同轴的限制结果，它允许我们将振动与光谱曲线的一般变形上定义的振动进行比较。

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A support theorem for\break the Hitchin fibration: The case of GLn and KC

Abstract We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for GLn{\mathrm{GL}_{n}} over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every n≥2{n\geq{2}}. A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over versal deformations of spectral curves.

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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.