{"title":"抛物线希格斯束的反常滤过、希尔伯特格式和P=W猜想","authors":"Junliang Shen, Zili Zhang","doi":"10.14231/AG-2021-014","DOIUrl":null,"url":null,"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.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2018-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Perverse filtrations, Hilbert schemes, and the $P=W$ Conjecture for parabolic Higgs bundles\",\"authors\":\"Junliang Shen, Zili Zhang\",\"doi\":\"10.14231/AG-2021-014\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":48564,\"journal\":{\"name\":\"Algebraic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2018-10-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.14231/AG-2021-014\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.14231/AG-2021-014","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Perverse filtrations, Hilbert schemes, and the $P=W$ Conjecture for parabolic Higgs bundles
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.
期刊介绍：
This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.
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