Infinitesimal deformations of some Quot schemes

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 spa...

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Veröffentlicht in:arXiv.org 2024-02
Hauptverfasser: Biswas, Indranil, Gangopadhyay, Chandranandan, Sebastian, Ronnie
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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 \(\mathcal{Q}(E,d)\).
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title Infinitesimal deformations of some Quot schemes
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