Quiver degeneracy loci via Schubert varieties


                 Ezra Miller (University of Minnesota)


Abstract:

Given a sequence E_0 --> E_1 --> ... --> E_n of morphisms of vector
bundles (a `quiver of vector bundles') on a fixed space X, what can
be said about its `degeneracy loci'?  These loci consist of the
points in X where the ranks of the composite morphisms E_i --> E_j
are bounded above by fixed integers r_ij for i < j.  Cohomological
and local geometric statements about degeneracy loci essentially
reduce to the corresponding statements about orbit closures of
certain group actions on vector spaces.  I will explain how to
deduce these statements using Zelevinsky's clever trick, which
relates everything to Schubert varieties.  Even though this talk
concerns the same joint work with Mark Shimozono and Allen Knutson
that I spoke about in September, I will not assume familiarity with
the objects or results that I discussed previously, and I will
define all of the above notions from scratch.