A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912688758587392 |
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| author | Gautam, Ajay Lin, Feiyang Sinha, Shubham |
| author_facet | Gautam, Ajay Lin, Feiyang Sinha, Shubham |
| contents | We study the cohomology groups of tautological bundles on Quot schemes over the projective line, which parametrize rank $r$ quotients of a vector bundle $V$ on $\mathbb{P}^1$. Our main result is an analogue of the Borel--Weil--Bott theorem for Quot schemes. As a corollary, we prove recent conjectures of Marian, Oprea, and Sam on the exterior and symmetric powers of tautological bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$ Gautam, Ajay Lin, Feiyang Sinha, Shubham Algebraic Geometry 14H60, 14M15, 14D20 14F08 We study the cohomology groups of tautological bundles on Quot schemes over the projective line, which parametrize rank $r$ quotients of a vector bundle $V$ on $\mathbb{P}^1$. Our main result is an analogue of the Borel--Weil--Bott theorem for Quot schemes. As a corollary, we prove recent conjectures of Marian, Oprea, and Sam on the exterior and symmetric powers of tautological bundles. |
| title | A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$ |
| topic | Algebraic Geometry 14H60, 14M15, 14D20 14F08 |
| url | https://arxiv.org/abs/2511.03519 |