Perverse filtrations, Hilbert schemes, and the $P=W$ Conjecture for parabolic Higgs bundles

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-10-12 DOI:10.14231/AG-2021-014

Junliang Shen, Zili Zhang

引用次数: 6

Abstract

We prove de Cataldo-Hausel-Migliorini's P=W conjecture in arbitrary rank for parabolic Higgs bundles labeled by the affine Dynkin diagrams $\tilde{A}_0$, $\tilde{D}_4$, $\tilde{E}_6$, $\tilde{E}_7$, and $\tilde{E}_8$. Our proof relies on the study of the tautological classes on the Hilbert scheme of points on an elliptic surface with respect to the perverse filtration.

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抛物线希格斯束的反常滤过、希尔伯特格式和P=W猜想

我们证明了由仿射Dynkin图$\tilde标记的抛物型Higgs丛的任意秩的de Cataldo Hauser Migliorini的P=W猜想{A}_0$，$\波浪号{D}_4$，$\波浪号{E}_6$，$\波浪号{E}_7$和$\波浪号{E}_8$。我们的证明依赖于关于反常过滤的椭圆表面上的点的Hilbert格式上的重言类的研究。

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

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