Free resolutions of some Schubert singularities in the Lagrangian Grassmannian

Venkatramani Lakshmibai and Reuven Hodges

Vol. 279 (2015), No. 1-2, 329–355

DOI: 10.2140/pjm.2015.279.329

Abstract

In this paper we construct free resolutions of a certain class of closed subvarieties of affine space of symmetric matrices (of a given size). Our class covers the symmetric determinantal varieties (i.e., determinantal varieties in the space of symmetric matrices), whose resolutions were first constructed by Józefiak, Pragacz and Weyman (1981). Our approach follows the techniques developed by Kummini, Lakshmibai, Pramathanath and Seshadri (2015), and uses the geometry of Schubert varieties.

Keywords

Schubert varieties, Lagrangian Grassmannian, free resolutions

Mathematical Subject Classification 2010

Primary: 20G20

Secondary: 14F05

Milestones

Received: 28 May 2015

Revised: 27 August 2015

Accepted: 28 September 2015

Published: 21 December 2015