Moduli of Abelian Varieties, Vinberg θ -Groups, and Free Resolutions
Identifieur interne : 000065 ( Main/Curation ); précédent : 000064; suivant : 000066Moduli of Abelian Varieties, Vinberg θ -Groups, and Free Resolutions
Auteurs : Laurent Gruson [France] ; Steven V. Sam [États-Unis] ; Jerzy Weyman [États-Unis]Source :
Abstract
Abstract: We present a systematic approach to studying the geometric aspects of Vinberg θ-representations. The main idea is to use the Borel-Weil construction for representations of reductive groups as sections of homogeneous bundles on homogeneous spaces, and then to study degeneracy loci of these vector bundles. Our main technical tool is to use free resolutions as an “enhanced” version of degeneracy loci formulas. We illustrate our approach on several examples and show how they are connected to moduli spaces of Abelian varieties. To make the article accessible to both algebraists and geometers, we also include background material on free resolutions and representation theory.
Url:
DOI: 10.1007/978-1-4614-5292-8_13
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: Pour aller vers cette notice dans l'étape Curation :001433
- to stream Istex, to step Curation: Pour aller vers cette notice dans l'étape Curation :001433
- to stream Istex, to step Checkpoint: Pour aller vers cette notice dans l'étape Curation :000036
- to stream Main, to step Merge: Pour aller vers cette notice dans l'étape Curation :000065
Links to Exploration step
ISTEX:62EA0E0D0341347FC87438C1D786FA0B2A07031CLe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Moduli of Abelian Varieties, Vinberg θ -Groups, and Free Resolutions</title>
<author><name sortKey="Gruson, Laurent" sort="Gruson, Laurent" uniqKey="Gruson L" first="Laurent" last="Gruson">Laurent Gruson</name>
</author>
<author><name sortKey="Sam, Steven V" sort="Sam, Steven V" uniqKey="Sam S" first="Steven V." last="Sam">Steven V. Sam</name>
</author>
<author><name sortKey="Weyman, Jerzy" sort="Weyman, Jerzy" uniqKey="Weyman J" first="Jerzy" last="Weyman">Jerzy Weyman</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:62EA0E0D0341347FC87438C1D786FA0B2A07031C</idno>
<date when="2013" year="2013">2013</date>
<idno type="doi">10.1007/978-1-4614-5292-8_13</idno>
<idno type="url">https://api.istex.fr/document/62EA0E0D0341347FC87438C1D786FA0B2A07031C/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001433</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001433</idno>
<idno type="wicri:Area/Istex/Curation">001433</idno>
<idno type="wicri:Area/Istex/Checkpoint">000036</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000036</idno>
<idno type="wicri:Area/Main/Merge">000065</idno>
<idno type="wicri:Area/Main/Curation">000065</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Moduli of Abelian Varieties, Vinberg θ -Groups, and Free Resolutions</title>
<author><name sortKey="Gruson, Laurent" sort="Gruson, Laurent" uniqKey="Gruson L" first="Laurent" last="Gruson">Laurent Gruson</name>
<affiliation wicri:level="4"><country xml:lang="fr">France</country>
<wicri:regionArea>Université de Versailles Saint-Quentin-en-Yvelines, Versailles</wicri:regionArea>
<placeName><region type="region">Île-de-France</region>
<region type="old region">Île-de-France</region>
<settlement type="city">Versailles</settlement>
<settlement type="city">Versailles</settlement>
</placeName>
<orgName type="university">Université de Versailles-Saint-Quentin-en-Yvelines</orgName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
</affiliation>
</author>
<author><name sortKey="Sam, Steven V" sort="Sam, Steven V" uniqKey="Sam S" first="Steven V." last="Sam">Steven V. Sam</name>
<affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country>
<wicri:regionArea>University of California, Berkeley, CA</wicri:regionArea>
<placeName><region type="state">Californie</region>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Weyman, Jerzy" sort="Weyman, Jerzy" uniqKey="Weyman J" first="Jerzy" last="Weyman">Jerzy Weyman</name>
<affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country>
<wicri:regionArea>Northeastern University, Boston, MA</wicri:regionArea>
<placeName><region type="state">Massachusetts</region>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: We present a systematic approach to studying the geometric aspects of Vinberg θ-representations. The main idea is to use the Borel-Weil construction for representations of reductive groups as sections of homogeneous bundles on homogeneous spaces, and then to study degeneracy loci of these vector bundles. Our main technical tool is to use free resolutions as an “enhanced” version of degeneracy loci formulas. We illustrate our approach on several examples and show how they are connected to moduli spaces of Abelian varieties. To make the article accessible to both algebraists and geometers, we also include background material on free resolutions and representation theory.</div>
</front>
</TEI>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000065 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Curation/biblio.hfd -nk 000065 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Main |étape= Curation |type= RBID |clé= ISTEX:62EA0E0D0341347FC87438C1D786FA0B2A07031C |texte= Moduli of Abelian Varieties, Vinberg θ -Groups, and Free Resolutions }}
This area was generated with Dilib version V0.6.33. |