$D$-affinity of Quadrics Revisited
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918296594415616 |
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| author | Rączka, Feliks |
| author_facet | Rączka, Feliks |
| contents | Let $K$ be aa algebraically closed field of characteristic $p\geq3$ and let $Q_{n}\subset\mathbb{P}^{n+1}_{K}$ be a smooth quadric hypersurface. We show that if $n=2m\geq4$ then $Q_{n}$ is not $D$-affine. In particular, we show the grassmannian ${Gr}(2,4)$ is not $D$-affine, which gives an example of a non $D$-affine flag variety of minimal possible dimension in characteristic $p\geq3$. Our result complements previous work of A. Langer, who showed that if $p\geq n=2m+1$ then $Q_{n}$ is $D$-affine. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13340 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $D$-affinity of Quadrics Revisited Rączka, Feliks Algebraic Geometry 14F10, 14M15, 14M17, 14G17 Let $K$ be aa algebraically closed field of characteristic $p\geq3$ and let $Q_{n}\subset\mathbb{P}^{n+1}_{K}$ be a smooth quadric hypersurface. We show that if $n=2m\geq4$ then $Q_{n}$ is not $D$-affine. In particular, we show the grassmannian ${Gr}(2,4)$ is not $D$-affine, which gives an example of a non $D$-affine flag variety of minimal possible dimension in characteristic $p\geq3$. Our result complements previous work of A. Langer, who showed that if $p\geq n=2m+1$ then $Q_{n}$ is $D$-affine. |
| title | $D$-affinity of Quadrics Revisited |
| topic | Algebraic Geometry 14F10, 14M15, 14M17, 14G17 |
| url | https://arxiv.org/abs/2601.13340 |