The variety of reductions for a reductive symmetric pair

The variety of reductions for a reductive symmetric pair

We define and study the variety of reductions for a reductive symmetric pair (G,theta), which is the natural compactification of the set of the Cartan subspaces of the symmetric pair. These varieties generalize the varieties of reductions for the Severi varieties studied by Iliev and Manivel, which...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2010-05
1. Verfasser: Michaël Le Barbier Grünewald
Format: Artikel
Sprache:eng
Schlagworte:
Deformation
Lie groups
Subspaces
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Michaël Le Barbier Grünewald
description We define and study the variety of reductions for a reductive symmetric pair (G,theta), which is the natural compactification of the set of the Cartan subspaces of the symmetric pair. These varieties generalize the varieties of reductions for the Severi varieties studied by Iliev and Manivel, which are Fano varieties. We develop a theoretical basis to the study these varieties of reductions, and relate the geometry of these variety to some problems in representation theory. A very useful result is the rigidity of semi-simple elements in deformations of algebraic subalgebras of Lie algebras. We apply this theory to the study of other varieties of reductions in a companion paper, which yields two new Fano varieties.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2087084537</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2087084537</sourcerecordid><originalsourceid>FETCH-proquest_journals_20870845373</originalsourceid><addsrcrecordid>eNqNikEKwjAQAIMgWLR_WPBciEljchfFB_ReQt3QFNvUTVLo7_Wgd08DM7NhhZDyVJlaiB0rYxw45-KshVKyYKbpERZLHtMKwQHhI3fJhymCCwT2JxaEuI4jJvIdzNbTgW2dfUYsv9yz4-3aXO7VTOGVMaZ2CJmmT2oFN5qbWkkt_7veV_U2Sw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2087084537</pqid></control><display><type>article</type><title>The variety of reductions for a reductive symmetric pair</title><source>Freely Accessible Journals</source><creator>Michaël Le Barbier Grünewald</creator><creatorcontrib>Michaël Le Barbier Grünewald</creatorcontrib><description>We define and study the variety of reductions for a reductive symmetric pair (G,theta), which is the natural compactification of the set of the Cartan subspaces of the symmetric pair. These varieties generalize the varieties of reductions for the Severi varieties studied by Iliev and Manivel, which are Fano varieties. We develop a theoretical basis to the study these varieties of reductions, and relate the geometry of these variety to some problems in representation theory. A very useful result is the rigidity of semi-simple elements in deformations of algebraic subalgebras of Lie algebras. We apply this theory to the study of other varieties of reductions in a companion paper, which yields two new Fano varieties.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Deformation ; Lie groups ; Subspaces</subject><ispartof>arXiv.org, 2010-05</ispartof><rights>2010. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</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>780,784</link.rule.ids></links><search><creatorcontrib>Michaël Le Barbier Grünewald</creatorcontrib><title>The variety of reductions for a reductive symmetric pair</title><title>arXiv.org</title><description>We define and study the variety of reductions for a reductive symmetric pair (G,theta), which is the natural compactification of the set of the Cartan subspaces of the symmetric pair. These varieties generalize the varieties of reductions for the Severi varieties studied by Iliev and Manivel, which are Fano varieties. We develop a theoretical basis to the study these varieties of reductions, and relate the geometry of these variety to some problems in representation theory. A very useful result is the rigidity of semi-simple elements in deformations of algebraic subalgebras of Lie algebras. We apply this theory to the study of other varieties of reductions in a companion paper, which yields two new Fano varieties.</description><subject>Deformation</subject><subject>Lie groups</subject><subject>Subspaces</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNikEKwjAQAIMgWLR_WPBciEljchfFB_ReQt3QFNvUTVLo7_Wgd08DM7NhhZDyVJlaiB0rYxw45-KshVKyYKbpERZLHtMKwQHhI3fJhymCCwT2JxaEuI4jJvIdzNbTgW2dfUYsv9yz4-3aXO7VTOGVMaZ2CJmmT2oFN5qbWkkt_7veV_U2Sw</recordid><startdate>20100505</startdate><enddate>20100505</enddate><creator>Michaël Le Barbier Grünewald</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20100505</creationdate><title>The variety of reductions for a reductive symmetric pair</title><author>Michaël Le Barbier Grünewald</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20870845373</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Deformation</topic><topic>Lie groups</topic><topic>Subspaces</topic><toplevel>online_resources</toplevel><creatorcontrib>Michaël Le Barbier Grünewald</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Michaël Le Barbier Grünewald</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>The variety of reductions for a reductive symmetric pair</atitle><jtitle>arXiv.org</jtitle><date>2010-05-05</date><risdate>2010</risdate><eissn>2331-8422</eissn><abstract>We define and study the variety of reductions for a reductive symmetric pair (G,theta), which is the natural compactification of the set of the Cartan subspaces of the symmetric pair. These varieties generalize the varieties of reductions for the Severi varieties studied by Iliev and Manivel, which are Fano varieties. We develop a theoretical basis to the study these varieties of reductions, and relate the geometry of these variety to some problems in representation theory. A very useful result is the rigidity of semi-simple elements in deformations of algebraic subalgebras of Lie algebras. We apply this theory to the study of other varieties of reductions in a companion paper, which yields two new Fano varieties.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2010-05
issn 2331-8422
language eng
recordid cdi_proquest_journals_2087084537
source Freely Accessible Journals
subjects Deformation
Lie groups
Subspaces
title The variety of reductions for a reductive symmetric pair
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-15T04%3A52%3A22IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=The%20variety%20of%20reductions%20for%20a%20reductive%20symmetric%20pair&rft.jtitle=arXiv.org&rft.au=Micha%C3%ABl%20Le%20Barbier%20Gr%C3%BCnewald&rft.date=2010-05-05&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2087084537%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2087084537&rft_id=info:pmid/&rfr_iscdi=true