Moduli of Abelian varieties, Vinberg theta-groups, and free resolutions

Details Moduli of Abelian varieties, Vinberg theta-groups, and free resolutions Moduli of Abelian varieties, Vinberg theta-groups, and free resolutions

2012-03-12

arxiv.org/abs/1203.2575v1

Mathematics

Algebraic Geometry

41 pages, uses tabmac.sty

Scientific paper

We present a systematic approach to studying the geometric aspects of Vinberg theta-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.

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