Vanishing cotangent cohomology for Pl\"ucker algebras
Jan Arthur Christophersen, Nathan Owen Ilten
TL;DR
This paper proves the vanishing of higher cotangent cohomology modules for Grassmannian coordinate rings in the Pl"ucker embedding using representation theory and Bott's theorem, also addressing a related cohomology question.
Contribution
It introduces a novel application of representation theory and Bott's theorem to cohomology vanishing problems in algebraic geometry, specifically for Pl"ucker algebras.
Findings
Higher cotangent cohomology modules vanish for Grassmannians in Pl"ucker embedding
Answers Wahl's question on cohomology of squared ideal sheaf for Pl"ucker relations
Provides new insights into the structure of Pl"ucker 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 Pl\"ucker embedding. As a biproduct we answer a question of Wahl about the cohomology of the square of the ideal sheaf for the case of Pl\"ucker relations.
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