Stability of sheaves over Quot schemes

Gangopadhyay, Chandranandan

doi:10.1016/j.bulsci.2018.08.001

Cited by 3 publications

(2 citation statements)

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“…In [Gan18] it was shown that when E ∼ = O n C for some n 1, the vector bundle A is stable with respect to certain polarizations on Q. In particular, H 0 (C × Q, E nd(A)) = 1 in that case.…”

Section: From Lemma 83 It Follows That Hmentioning

confidence: 99%

“…In [Gan18] it was shown that when E ∼ = O n C for some n 1, then A is slope stable with respect to some natural polarizations of C × Q. By [HL10, Corollary 4.5.2], H 1 (C × Q, E nd(A)) is the tangent space of the Moduli space M of sheaves on C × Q with the same Hilbert polynomial (with respect to some fixed polarization on C × Q) as A.…”

Section: Introductionmentioning

confidence: 99%

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Infinitesimal deformations of some Quot schemes

Biswas¹,

Gangopadhyay²,

Sebastian³

2022

Preprint

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Let E be a vector bundle on a smooth complex projective curve C of genus at least two. Let 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 Q(E,d) . In particular, the space of infinitesimal deformations of Q(E, d) is computed. Kempf and Fantechi computed the space of infinitesimal deformations of]). We also explicitly describe the infinitesimal deformations of Q(E, d).

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Section: From Lemma 83 It Follows That Hmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Infinitesimal deformations of some Quot schemes

Biswas¹,

Gangopadhyay²,

Sebastian³

2022

Preprint

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Automorphisms of relative Quot schemes

Gangopadhyay

2019

Proc Math Sci

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Let X, S be two smooth projective varieties and X → S be a smooth family of projective curves of genus ≥ 2 over an algebraically closed field k and let E be a vector bundle of rank r ≥ 3 over X and P(E) be its projectivization. Fix d ≥ 1. Let Q(E, d) be the relative quot scheme of torsion quotients of E of degree d. Then we show that the identity component of the group of automorphisms of Q(E, d) over S is isomorphic to the identity component of the group of automorphisms of P(E) over S. As a corollary, the identity component of the automorphism group of flag scheme of filtrations of torsion quotients of O r C , where r ≥ 3 and C a smooth projective curve of genus ≥ 2 is computed.

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Infinitesimal Deformations of Some Quot Schemes

Biswas,

Gangopadhyay,

Sebastian

2024

International Mathematics Research Notices

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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 $\mathcal{Q}({\mathcal O}_{C},d)\,=\, C^{(d)}$ [ 11, 19].

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Stability of sheaves over Quot schemes

Cited by 3 publications

References 1 publication

Infinitesimal deformations of some Quot schemes

Infinitesimal deformations of some Quot schemes

Automorphisms of relative Quot schemes

Infinitesimal Deformations of Some Quot Schemes

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