Infinitesimal deformations of some Quot schemes
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 infini...
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| creator | Biswas, Indranil Gangopadhyay, Chandranandan Sebastian, Ronnie |
| description | 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 $\mathcal{Q}(E,d)$. |
| doi_str_mv | 10.48550/arxiv.2203.13150 |
| format | Article |
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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 $\mathcal{Q}(E,d)$.</description><identifier>DOI: 10.48550/arxiv.2203.13150</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry</subject><creationdate>2022-03</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2203.13150$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2203.13150$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Biswas, Indranil</creatorcontrib><creatorcontrib>Gangopadhyay, Chandranandan</creatorcontrib><creatorcontrib>Sebastian, Ronnie</creatorcontrib><title>Infinitesimal deformations of some Quot schemes</title><description>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
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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 $\mathcal{Q}(E,d)$.</abstract><doi>10.48550/arxiv.2203.13150</doi><oa>free_for_read</oa></addata></record> |
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| title | Infinitesimal deformations of some Quot schemes |
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