The variety of reductions for a reductive symmetric pair
Identifieur interne : 000370 ( Main/Exploration ); précédent : 000369; suivant : 000371The variety of reductions for a reductive symmetric pair
Auteurs : Michaël Le Barbier Grünewald [Allemagne]Source :
- Transformation Groups [ 1083-4362 ] ; 2011-03-01.
Abstract
Abstract: We define and study the variety of reductions for a complex reductive symmetric pair (G, θ), which is the natural compactification of the set of its Cartan subspaces. 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 of these varieties of reductions, and relate their geometry to some problems in representation theory. A very useful result is the rigidity of semisimple elements in deformations of algebraic subalgebras of Lie algebras. We use it to show that the closure of a decomposition class is a union of decomposition classes. We apply this theory to the study of other varieties of reductions in a companion paper, which yields two new Fano varieties.
Url:
DOI: 10.1007/s00031-010-9108-3
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001174
- to stream Istex, to step Curation: 001174
- to stream Istex, to step Checkpoint: 000325
- to stream Main, to step Merge: 000369
- to stream Main, to step Curation: 000370
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">The variety of reductions for a reductive symmetric pair</title>
<author><name sortKey="Le Barbier Grunewald, Michael" sort="Le Barbier Grunewald, Michael" uniqKey="Le Barbier Grunewald M" first="Michaël" last="Le Barbier Grünewald">Michaël Le Barbier Grünewald</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:561F7DFEFD883375C42FB40B9E568BC776F061BC</idno>
<date when="2010" year="2010">2010</date>
<idno type="doi">10.1007/s00031-010-9108-3</idno>
<idno type="url">https://api.istex.fr/document/561F7DFEFD883375C42FB40B9E568BC776F061BC/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001174</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001174</idno>
<idno type="wicri:Area/Istex/Curation">001174</idno>
<idno type="wicri:Area/Istex/Checkpoint">000325</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000325</idno>
<idno type="wicri:doubleKey">1083-4362:2010:Le Barbier Grunewald M:the:variety:of</idno>
<idno type="wicri:Area/Main/Merge">000369</idno>
<idno type="wicri:Area/Main/Curation">000370</idno>
<idno type="wicri:Area/Main/Exploration">000370</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">The variety of reductions for a reductive symmetric pair</title>
<author><name sortKey="Le Barbier Grunewald, Michael" sort="Le Barbier Grunewald, Michael" uniqKey="Le Barbier Grunewald M" first="Michaël" last="Le Barbier Grünewald">Michaël Le Barbier Grünewald</name>
<affiliation wicri:level="3"><country xml:lang="fr">Allemagne</country>
<wicri:regionArea>Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53 111, Bonn</wicri:regionArea>
<placeName><region type="land" nuts="1">Rhénanie-du-Nord-Westphalie</region>
<region type="district" nuts="2">District de Cologne</region>
<settlement type="city">Bonn</settlement>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">Allemagne</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Transformation Groups</title>
<title level="j" type="abbrev">Transformation Groups</title>
<idno type="ISSN">1083-4362</idno>
<idno type="eISSN">1531-586X</idno>
<imprint><publisher>SP Birkhäuser Verlag Boston</publisher>
<pubPlace>Boston</pubPlace>
<date type="published" when="2011-03-01">2011-03-01</date>
<biblScope unit="volume">16</biblScope>
<biblScope unit="issue">1</biblScope>
<biblScope unit="page" from="1">1</biblScope>
<biblScope unit="page" to="26">26</biblScope>
</imprint>
<idno type="ISSN">1083-4362</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">1083-4362</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: We define and study the variety of reductions for a complex reductive symmetric pair (G, θ), which is the natural compactification of the set of its Cartan subspaces. 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 of these varieties of reductions, and relate their geometry to some problems in representation theory. A very useful result is the rigidity of semisimple elements in deformations of algebraic subalgebras of Lie algebras. We use it to show that the closure of a decomposition class is a union of decomposition classes. We apply this theory to the study of other varieties of reductions in a companion paper, which yields two new Fano varieties.</div>
</front>
</TEI>
<affiliations><list><country><li>Allemagne</li>
</country>
<region><li>District de Cologne</li>
<li>Rhénanie-du-Nord-Westphalie</li>
</region>
<settlement><li>Bonn</li>
</settlement>
</list>
<tree><country name="Allemagne"><region name="Rhénanie-du-Nord-Westphalie"><name sortKey="Le Barbier Grunewald, Michael" sort="Le Barbier Grunewald, Michael" uniqKey="Le Barbier Grunewald M" first="Michaël" last="Le Barbier Grünewald">Michaël Le Barbier Grünewald</name>
</region>
<name sortKey="Le Barbier Grunewald, Michael" sort="Le Barbier Grunewald, Michael" uniqKey="Le Barbier Grunewald M" first="Michaël" last="Le Barbier Grünewald">Michaël Le Barbier Grünewald</name>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000370 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000370 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:561F7DFEFD883375C42FB40B9E568BC776F061BC |texte= The variety of reductions for a reductive symmetric pair }}
This area was generated with Dilib version V0.6.33. |