6 research outputs found
Moduli of Abelian varieties, Vinberg theta-groups, and free resolutions
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.Comment: 41 pages, uses tabmac.sty, Dedicated to David Eisenbud on the
occasion of his 65th birthday; v2: fixed some typos and added reference
Four lectures on secant varieties
This paper is based on the first author's lectures at the 2012 University of
Regina Workshop "Connections Between Algebra and Geometry". Its aim is to
provide an introduction to the theory of higher secant varieties and their
applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in
Mathematics & Statistics), Springer/Birkhause