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.

KEYWORDS:

• Cotangent cohomology
• Grassmannians
• local cohomology

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 14M15
• Secondary 14B15
• 14D15
• 13D03

Acknowledgment

We would like to thank Steven Sam for helpful discussions on representation theory.