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arXiv · 2506.09727

Hochschild Cohomology of Isotropic Grassmannians

Anton Fonarev
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Abstract

We prove that nonspecial isotropic Grassmannians (that is, all isotropic Grassmannians which are neither (co)adjoint nor (co)minuscule, except $\mathsf{OGr}(n-1, 2n+1)$ for $n\geq 4$), are not Hochschild global, thus establishing a conjecture by P. Belmans and M. Smirnov. As a corollary, we conclude that Bott vanishing fails for all these varieties.

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Anton Fonarev. 2025-06-11. Hochschild Cohomology of Isotropic Grassmannians. https://arxiv.org/abs/2506.09727

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