Moduli of Abelian Varieties, Vinberg θ-Groups, and Free Resolutions

Laurent Gruson (), Steven V. Sam () and Jerzy Weyman ()
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Laurent Gruson: Université de Versailles Saint-Quentin-en-Yvelines
Steven V. Sam: University of California
Jerzy Weyman: Northeastern University

A chapter in Commutative Algebra, 2013, pp 419-469 from Springer

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.

Keywords: Modulus Space; Vector Bundle; Abelian Variety; Dynkin Diagram; Orbit Closure (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-5292-8_13

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DOI: 10.1007/978-1-4614-5292-8_13

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