Infinitesimal deformations of some Quot schemes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913225364209664 |
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| author | Biswas, Indranil Gangopadhyay, Chandranandan Sebastian, Ronnie |
| author_facet | Biswas, Indranil Gangopadhyay, Chandranandan Sebastian, Ronnie |
| contents | Let $E$ be a vector bundle on a smooth complex projective curve $C$ of genus at least two. Let $\mathcal{Q}(E,d)$ be the Quot scheme parameterizing the torsion quotients of $E$ of degree $d$. We compute the cohomologies of the tangent bundle $T_{\mathcal{Q}(E,d)}$. In particular, the space of infinitesimal deformations of $\mathcal{Q}(E,d)$ is computed. Kempf and Fantechi computed the space of infinitesimal deformations of $\mathcal{Q}(\mathcal{O}_C,d)\,=\, C^{(d)}$. We also explicitly describe the infinitesimal deformations of $\mathcal{Q}(E,d)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_13150 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Infinitesimal deformations of some Quot schemes Biswas, Indranil Gangopadhyay, Chandranandan Sebastian, Ronnie Algebraic Geometry 14J60, 32G05, 14J50, 14D15 Let $E$ be a vector bundle on a smooth complex projective curve $C$ of genus at least two. Let $\mathcal{Q}(E,d)$ be the Quot scheme parameterizing the torsion quotients of $E$ of degree $d$. We compute the cohomologies of the tangent bundle $T_{\mathcal{Q}(E,d)}$. In particular, the space of infinitesimal deformations of $\mathcal{Q}(E,d)$ is computed. Kempf and Fantechi computed the space of infinitesimal deformations of $\mathcal{Q}(\mathcal{O}_C,d)\,=\, C^{(d)}$. We also explicitly describe the infinitesimal deformations of $\mathcal{Q}(E,d)$. |
| title | Infinitesimal deformations of some Quot schemes |
| topic | Algebraic Geometry 14J60, 32G05, 14J50, 14D15 |
| url | https://arxiv.org/abs/2203.13150 |