Moduli of Abelian Varieties, Vinberg θ -Groups, and Free Resolutions
Identifieur interne : 000065 ( Main/Exploration ); 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
Affiliations:
- France, États-Unis
- Californie, Massachusetts, Île-de-France
- Versailles
- Université de Versailles-Saint-Quentin-en-Yvelines
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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. 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Sam</name></region><name sortKey="Sam, Steven V" sort="Sam, Steven V" uniqKey="Sam S" first="Steven V." last="Sam">Steven V. Sam</name><name sortKey="Weyman, Jerzy" sort="Weyman, Jerzy" uniqKey="Weyman J" first="Jerzy" last="Weyman">Jerzy Weyman</name><name sortKey="Weyman, Jerzy" sort="Weyman, Jerzy" uniqKey="Weyman J" first="Jerzy" last="Weyman">Jerzy Weyman</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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