Minimal-Degree Foliations on Cominuscule Grassmannians
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914512433577984 |
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| author | Benedetti, Vladimiro Kuster, Crislaine Muniz, Alan |
| author_facet | Benedetti, Vladimiro Kuster, Crislaine Muniz, Alan |
| contents | Given $X$ a cominuscule Grassmannian (or irreducible Hermitian symmetric space) and an integer $p,$ we compute the minimum $l(p)$ such that $H^0 (Ω^p_X (l(p)))$ is not 0. This allows us to conclude that any codimension-one foliation of degree zero on a cominuscule Grassmannian is a pencil of hyperplanes, improving a result of the first and third authors with D. Faenzi. We also deduce the structure of codimension-one foliations of degree one. Finally, we provide families of examples of high codimensional foliations of minimal degree on classical Grassmannians, Lagrangian Grassmannians, Spinor varieties, and the Cayley plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal-Degree Foliations on Cominuscule Grassmannians Benedetti, Vladimiro Kuster, Crislaine Muniz, Alan Algebraic Geometry Given $X$ a cominuscule Grassmannian (or irreducible Hermitian symmetric space) and an integer $p,$ we compute the minimum $l(p)$ such that $H^0 (Ω^p_X (l(p)))$ is not 0. This allows us to conclude that any codimension-one foliation of degree zero on a cominuscule Grassmannian is a pencil of hyperplanes, improving a result of the first and third authors with D. Faenzi. We also deduce the structure of codimension-one foliations of degree one. Finally, we provide families of examples of high codimensional foliations of minimal degree on classical Grassmannians, Lagrangian Grassmannians, Spinor varieties, and the Cayley plane. |
| title | Minimal-Degree Foliations on Cominuscule Grassmannians |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.05553 |