Free resolutions of some Schubert singularities

Manoj Kummini, Venkatramani Lakshmibai, Pramathanath Sastry and C. S. Seshadri

Vol. 279 (2015), No. 1-2, 299–328

DOI: 10.2140/pjm.2015.279.299

Abstract

In this paper we construct free resolutions of a class of 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. in Math. 30:3 (1978), 202–237). 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.

Keywords

Schubert singularities, free resolutions

Mathematical Subject Classification 2010

Primary: 14M15, 13D02, 14H05

Secondary: 14J17, 15A03

Milestones

Received: 16 April 2015

Revised: 21 June 2015

Accepted: 8 October 2015

Published: 21 December 2015