Vanishing cotangent cohomology for Plücker algebras

Abstract

We use representation theory and Bott’s theorem to show vanishing of higher cotangent cohomology modules for the homogeneous coordinate ring of Grassmannians in the Plücker embedding. As a by-product, we answer a question of Wahl about the cohomology of the square of the ideal sheaf for the case of Plücker relations. We obtain slightly weaker vanishing results for the cotangent cohomology of the coordinate rings of isotropic Grassmannians. This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 31 Jan 2017, available online: http://www.tandfonline.com/10.1080/00927872.2016.1249373