Hochschild Cohomology of Isotropic Grassmannians
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916790663118848 |
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| author | Fonarev, Anton |
| author_facet | Fonarev, Anton |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hochschild Cohomology of Isotropic Grassmannians Fonarev, Anton Algebraic Geometry 14M15, 14F17 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. |
| title | Hochschild Cohomology of Isotropic Grassmannians |
| topic | Algebraic Geometry 14M15, 14F17 |
| url | https://arxiv.org/abs/2506.09727 |