Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties

Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties

We prove several results on symplectic varieties with a Hamiltonian action of a reductive group having invariant Lagrangian subvarieties. Our main result states that the images of the moment maps of a Hamiltonian variety and of the cotangent bundle over an invariant Lagrangian subvariety coincide. T...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Timashev, Dmitry A, Zhgoon, Vladimir S
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Algebraic Geometry
Mathematics - Symplectic Geometry
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Timashev, Dmitry A
Zhgoon, Vladimir S
description We prove several results on symplectic varieties with a Hamiltonian action of a reductive group having invariant Lagrangian subvarieties. Our main result states that the images of the moment maps of a Hamiltonian variety and of the cotangent bundle over an invariant Lagrangian subvariety coincide. This implies that the complexity and rank of the Lagrangian subvariety are equal to the half of the corank and to the defect of the Hamiltonian variety, respectively. This result generalizes a theorem of Panyushev on the complexity and rank of a conormal bundle. A simple elementary proof of this theorem is also given in the paper. A generalization of the above results to some special class of invariant coisotropic subvarieties is obtained.
doi_str_mv 10.48550/arxiv.1109.5239
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1109_5239</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1109_5239</sourcerecordid><originalsourceid>FETCH-LOGICAL-a659-183815f2879ae0d8826ac88f6bc8914d38fb02db9372972d965cae25f590c01e3</originalsourceid><addsrcrecordid>eNo9j8tqwzAURLXpoqTdd1X0A3b0iOyrZQhpUzAUSvbmWpYSgS0HSc3j71u3pathhpmBQ8gTZ-UKlGJLjFd_LjlnulRC6nvyscPRD3kKHgNFk_0UEp0CTbfxNNhvb-gZo7fZ20QvPh-pD3OAIdMGDxHDYV6mz-6_9kDuHA7JPv7pguxftvvNrmjeX98266bASumCgwSunIBao2U9gKjQALiqM6D5qpfgOib6Tsta6Fr0ulIGrVBOaWYYt3JBnn9vf5jaU_Qjxls7s7Uzm_wCSUtK4w</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties</title><source>arXiv.org</source><creator>Timashev, Dmitry A ; Zhgoon, Vladimir S</creator><creatorcontrib>Timashev, Dmitry A ; Zhgoon, Vladimir S</creatorcontrib><description>We prove several results on symplectic varieties with a Hamiltonian action of a reductive group having invariant Lagrangian subvarieties. Our main result states that the images of the moment maps of a Hamiltonian variety and of the cotangent bundle over an invariant Lagrangian subvariety coincide. This implies that the complexity and rank of the Lagrangian subvariety are equal to the half of the corank and to the defect of the Hamiltonian variety, respectively. This result generalizes a theorem of Panyushev on the complexity and rank of a conormal bundle. A simple elementary proof of this theorem is also given in the paper. A generalization of the above results to some special class of invariant coisotropic subvarieties is obtained.</description><identifier>DOI: 10.48550/arxiv.1109.5239</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry ; Mathematics - Symplectic Geometry</subject><creationdate>2011-09</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1109.5239$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1109.5239$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Timashev, Dmitry A</creatorcontrib><creatorcontrib>Zhgoon, Vladimir S</creatorcontrib><title>Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties</title><description>We prove several results on symplectic varieties with a Hamiltonian action of a reductive group having invariant Lagrangian subvarieties. Our main result states that the images of the moment maps of a Hamiltonian variety and of the cotangent bundle over an invariant Lagrangian subvariety coincide. This implies that the complexity and rank of the Lagrangian subvariety are equal to the half of the corank and to the defect of the Hamiltonian variety, respectively. This result generalizes a theorem of Panyushev on the complexity and rank of a conormal bundle. A simple elementary proof of this theorem is also given in the paper. A generalization of the above results to some special class of invariant coisotropic subvarieties is obtained.</description><subject>Mathematics - Algebraic Geometry</subject><subject>Mathematics - Symplectic Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNo9j8tqwzAURLXpoqTdd1X0A3b0iOyrZQhpUzAUSvbmWpYSgS0HSc3j71u3pathhpmBQ8gTZ-UKlGJLjFd_LjlnulRC6nvyscPRD3kKHgNFk_0UEp0CTbfxNNhvb-gZo7fZ20QvPh-pD3OAIdMGDxHDYV6mz-6_9kDuHA7JPv7pguxftvvNrmjeX98266bASumCgwSunIBao2U9gKjQALiqM6D5qpfgOib6Tsta6Fr0ulIGrVBOaWYYt3JBnn9vf5jaU_Qjxls7s7Uzm_wCSUtK4w</recordid><startdate>20110924</startdate><enddate>20110924</enddate><creator>Timashev, Dmitry A</creator><creator>Zhgoon, Vladimir S</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20110924</creationdate><title>Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties</title><author>Timashev, Dmitry A ; Zhgoon, Vladimir S</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a659-183815f2879ae0d8826ac88f6bc8914d38fb02db9372972d965cae25f590c01e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Mathematics - Algebraic Geometry</topic><topic>Mathematics - Symplectic Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Timashev, Dmitry A</creatorcontrib><creatorcontrib>Zhgoon, Vladimir S</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Timashev, Dmitry A</au><au>Zhgoon, Vladimir S</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties</atitle><date>2011-09-24</date><risdate>2011</risdate><abstract>We prove several results on symplectic varieties with a Hamiltonian action of a reductive group having invariant Lagrangian subvarieties. Our main result states that the images of the moment maps of a Hamiltonian variety and of the cotangent bundle over an invariant Lagrangian subvariety coincide. This implies that the complexity and rank of the Lagrangian subvariety are equal to the half of the corank and to the defect of the Hamiltonian variety, respectively. This result generalizes a theorem of Panyushev on the complexity and rank of a conormal bundle. A simple elementary proof of this theorem is also given in the paper. A generalization of the above results to some special class of invariant coisotropic subvarieties is obtained.</abstract><doi>10.48550/arxiv.1109.5239</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.1109.5239
ispartof
issn
language eng
recordid cdi_arxiv_primary_1109_5239
source arXiv.org
subjects Mathematics - Algebraic Geometry
Mathematics - Symplectic Geometry
title Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-29T10%3A13%3A43IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Hamiltonian%20actions%20on%20symplectic%20varieties%20with%20invariant%20Lagrangian%20subvarieties&rft.au=Timashev,%20Dmitry%20A&rft.date=2011-09-24&rft_id=info:doi/10.48550/arxiv.1109.5239&rft_dat=%3Carxiv_GOX%3E1109_5239%3C/arxiv_GOX%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