Hodge-to-singular correspondence for reduced curves

Hodge-to-singular correspondence for reduced curves

We study the summands of the decomposition theorem for the Hitchin system for \operatorname{GL}_{n} , in arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new correspondence between these summands and the topology of hypertoric quiver varieties. In contrast to the ca...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2024-07
Hauptverfasser: Mauri, Mirko, Migliorini, Luca
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title Journal of the European Mathematical Society : JEMS
container_volume
creator Mauri, Mirko
Migliorini, Luca
description We study the summands of the decomposition theorem for the Hitchin system for \operatorname{GL}_{n} , in arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new correspondence between these summands and the topology of hypertoric quiver varieties. In contrast to the case of meromorphic Higgs fields, the intersection cohomology groups of moduli spaces of regular Higgs bundles depend on the degree. We describe this dependence.
doi_str_mv 10.4171/jems/1508
format Article
fullrecord <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_4171_jems_1508</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_4171_jems_1508</sourcerecordid><originalsourceid>FETCH-LOGICAL-c698-406f204b267627bfc0e24203fcc15eceef7200fc6896e0e0b8b1d2ad541cd3293</originalsourceid><addsrcrecordid>eNo9z01LAzEUheEgFqy1C__BbF3E3nxnllLUFgpuug8zNzelpZ2UxBH89zIors67OvAw9ijgWQsnVie61JUw4G_YXGhleOutuv1vY-7Yfa0nAOGMVnOmNjkeiH9mXo_DYTx3pcFcCtVrHiINSE3KpSkUR6TY4Fi-qD6wWerOlZZ_u2D7t9f9esN3H-_b9cuOo20912CTBN1L66x0fUIgqSWohCgMIVFyEiCh9a0lIOh9L6LsotECo5KtWrCn31ssudZCKVzL8dKV7yAgTNgwYcOEVT9sLUf1</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Hodge-to-singular correspondence for reduced curves</title><source>DOAJ Directory of Open Access Journals</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Mauri, Mirko ; Migliorini, Luca</creator><creatorcontrib>Mauri, Mirko ; Migliorini, Luca</creatorcontrib><description>We study the summands of the decomposition theorem for the Hitchin system for \operatorname{GL}_{n} , in arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new correspondence between these summands and the topology of hypertoric quiver varieties. In contrast to the case of meromorphic Higgs fields, the intersection cohomology groups of moduli spaces of regular Higgs bundles depend on the degree. We describe this dependence.</description><identifier>ISSN: 1435-9855</identifier><identifier>EISSN: 1435-9863</identifier><identifier>DOI: 10.4171/jems/1508</identifier><language>eng</language><ispartof>Journal of the European Mathematical Society : JEMS, 2024-07</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0002-1570-2078</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,864,27924,27925</link.rule.ids></links><search><creatorcontrib>Mauri, Mirko</creatorcontrib><creatorcontrib>Migliorini, Luca</creatorcontrib><title>Hodge-to-singular correspondence for reduced curves</title><title>Journal of the European Mathematical Society : JEMS</title><description>We study the summands of the decomposition theorem for the Hitchin system for \operatorname{GL}_{n} , in arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new correspondence between these summands and the topology of hypertoric quiver varieties. In contrast to the case of meromorphic Higgs fields, the intersection cohomology groups of moduli spaces of regular Higgs bundles depend on the degree. We describe this dependence.</description><issn>1435-9855</issn><issn>1435-9863</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNo9z01LAzEUheEgFqy1C__BbF3E3nxnllLUFgpuug8zNzelpZ2UxBH89zIors67OvAw9ijgWQsnVie61JUw4G_YXGhleOutuv1vY-7Yfa0nAOGMVnOmNjkeiH9mXo_DYTx3pcFcCtVrHiINSE3KpSkUR6TY4Fi-qD6wWerOlZZ_u2D7t9f9esN3H-_b9cuOo20912CTBN1L66x0fUIgqSWohCgMIVFyEiCh9a0lIOh9L6LsotECo5KtWrCn31ssudZCKVzL8dKV7yAgTNgwYcOEVT9sLUf1</recordid><startdate>20240723</startdate><enddate>20240723</enddate><creator>Mauri, Mirko</creator><creator>Migliorini, Luca</creator><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-1570-2078</orcidid></search><sort><creationdate>20240723</creationdate><title>Hodge-to-singular correspondence for reduced curves</title><author>Mauri, Mirko ; Migliorini, Luca</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c698-406f204b267627bfc0e24203fcc15eceef7200fc6896e0e0b8b1d2ad541cd3293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mauri, Mirko</creatorcontrib><creatorcontrib>Migliorini, Luca</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of the European Mathematical Society : JEMS</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mauri, Mirko</au><au>Migliorini, Luca</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hodge-to-singular correspondence for reduced curves</atitle><jtitle>Journal of the European Mathematical Society : JEMS</jtitle><date>2024-07-23</date><risdate>2024</risdate><issn>1435-9855</issn><eissn>1435-9863</eissn><abstract>We study the summands of the decomposition theorem for the Hitchin system for \operatorname{GL}_{n} , in arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new correspondence between these summands and the topology of hypertoric quiver varieties. In contrast to the case of meromorphic Higgs fields, the intersection cohomology groups of moduli spaces of regular Higgs bundles depend on the degree. We describe this dependence.</abstract><doi>10.4171/jems/1508</doi><orcidid>https://orcid.org/0000-0002-1570-2078</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1435-9855
ispartof Journal of the European Mathematical Society : JEMS, 2024-07
issn 1435-9855
1435-9863
language eng
recordid cdi_crossref_primary_10_4171_jems_1508
source DOAJ Directory of Open Access Journals; EZB-FREE-00999 freely available EZB journals
title Hodge-to-singular correspondence for reduced curves
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T18%3A52%3A34IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Hodge-to-singular%20correspondence%20for%20reduced%20curves&rft.jtitle=Journal%20of%20the%20European%20Mathematical%20Society%20:%20JEMS&rft.au=Mauri,%20Mirko&rft.date=2024-07-23&rft.issn=1435-9855&rft.eissn=1435-9863&rft_id=info:doi/10.4171/jems/1508&rft_dat=%3Ccrossref%3E10_4171_jems_1508%3C/crossref%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true