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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.08695 |
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| _version_ | 1866915863462936576 |
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| author | Marian, Alina Neguţ, Andrei |
| author_facet | Marian, Alina Neguţ, Andrei |
| contents | We define a categorical action of the shifted quantum loop group of $\mathfrak{sl}_2$ on the derived categories of Quot schemes of finite length quotient sheaves on a smooth projective curve. As an application, we obtain a semi-orthogonal decomposition of the derived categories of Quot schemes, of representation theoretic origin. We use this decomposition to calculate the cohomology of interesting tautological vector bundles over the Quot scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derived categories of Quot schemes on smooth curves and tautological bundles Marian, Alina Neguţ, Andrei Algebraic Geometry Representation Theory We define a categorical action of the shifted quantum loop group of $\mathfrak{sl}_2$ on the derived categories of Quot schemes of finite length quotient sheaves on a smooth projective curve. As an application, we obtain a semi-orthogonal decomposition of the derived categories of Quot schemes, of representation theoretic origin. We use this decomposition to calculate the cohomology of interesting tautological vector bundles over the Quot scheme. |
| title | Derived categories of Quot schemes on smooth curves and tautological bundles |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2411.08695 |