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

In: Commutative Algebra

Author

Listed:
  • Laurent Gruson

    (Université de Versailles Saint-Quentin-en-Yvelines)

  • Steven V. Sam

    (University of California)

  • Jerzy Weyman

    (Northeastern University)

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.

Suggested Citation

  • Laurent Gruson & Steven V. Sam & Jerzy Weyman, 2013. "Moduli of Abelian Varieties, Vinberg θ-Groups, and Free Resolutions," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, edition 127, pages 419-469, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-5292-8_13
    DOI: 10.1007/978-1-4614-5292-8_13
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