Hall 123

Free resolutions of some Schubert singularities

V. Lakshmibai

Northeastern University, Boston

We construct free resolutions of certain closed subvarieties of
affine spaces (the so called “opposite big cells” of Grassmannians). Our
class covers the determinantal varieties, whose resolutions were first
constructed by A. Lascoux (Adv. Math., 1978). Our approach uses the geometry
of Schubert
varieties. An interesting aspect of our work is its connection to the
computation of the cohomology of homogeneous bundles (that are not
necessarily completely reducible) on partial flag varieties.
This work is jointly with M. Kummini, P.Sastry &C.S. Seshadri.