Fundamental group schemes of some Quot schemes on a smooth projective curve

Gangopadhyay, Chandranandan; Sebastian, Ronnie

doi:10.1016/j.jalgebra.2020.06.025

Cited by 7 publications

(7 citation statements)

References 7 publications

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“…Therefore, we have the pullback Φ * : Pic(C (d ) ) → Pic(Q) which is in fact an inclusion. To see this, recall that the fibres of Φ are projective integral varieties [8, Corollary 6.6] and Φ is flat [8,Corollary 6.3 (d ) ) and the statement follows.…”

Section: Picard Group and Neron-severi Group Of Qmentioning

confidence: 99%

“…In [7], the automorphism group scheme of Q(E , d ) was computed in the case when either rk E ≥ 3 or E is semistable and genus of C satisfies g (C ) > 1. In [8], the S-fundamental group scheme of Q(E , d ) was computed.…”

Section: Introductionmentioning

confidence: 99%

“…Recall that we have a Hilbert-Chow map Φ : Q → C (d ) (this map is explained after Definition 9. A precise definition can be found, for example, in [8]). For notational convenience, for a divisor D ∈ N 1 (C (d ) ) we will denote its pullback Φ * D ∈ N 1 (Q) by D, when there is no possibility of confusion.…”

Section: Introductionmentioning

confidence: 99%

“…By[8, Corollary 6.3] and[8, Corollary 6.4] the morphism Φ is flat and fibres of Φ are integral. Then by[13, Lemma 2.1.2] and Lemma 10 we get that L…”

mentioning

confidence: 99%

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Nef cones of some Quot schemes on a Smooth Projective Curve

Gangopadhyay¹,

Sebastian²

2021

Comptes Rendus. Mathématique

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Let C be a smooth projective curve over C. Let n, d ≥ 1. Let Q be the Quot scheme parameterizing torsion quotients of the vector bundle O n C of degree d . In this article we study the nef cone of Q. We give a complete description of the nef cone in the case of elliptic curves. We compute it in the case when d = 2 and C very general, in terms of the nef cone of the second symmetric product of C . In the case when n ≥ d and C very general, we give upper and lower bounds for the Nef cone. In general, we give a necessary and sufficient criterion for a divisor on Q to be nef.

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Section: Picard Group and Neron-severi Group Of Qmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…By[8, Corollary 6.3] and[8, Corollary 6.4] the morphism Φ is flat and fibres of Φ are integral. Then by[13, Lemma 2.1.2] and Lemma 10 we get that L…”

mentioning

confidence: 99%

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Nef cones of some Quot schemes on a Smooth Projective Curve

Gangopadhyay¹,

Sebastian²

2021

Comptes Rendus. Mathématique

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“…In these sections we show that the relative adjoint Atiyah sequence associated to a vector bundle V on C × X (see (4.4)), restricted to c × X can be obtained in three different ways. In Section 6 we recall the construction of the space S d from [GS20] and prove a result relating to its canonical divisor. In Section 7 we prove some results related to projective bundles.…”

Section: Introductionmentioning

confidence: 99%

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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Irreducibility of Lagrangian Quot schemes over an algebraic curve

2021

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Let C be a complex projective smooth curve and W a symplectic vector bundle of rank 2n over C. The Lagrangian Quot scheme $$LQ_{-e}(W)$$ L Q - e ( W ) parameterizes subsheaves of rank n and degree $$-e$$ - e which are isotropic with respect to the symplectic form. We prove that $$LQ_{-e}(W)$$ L Q - e ( W ) is irreducible and generically smooth of the expected dimension for all large e, and that a generic element is saturated and stable.

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Fundamental group schemes of some Quot schemes on a smooth projective curve

Cited by 7 publications

References 7 publications

Nef cones of some Quot schemes on a Smooth Projective Curve

Nef cones of some Quot schemes on a Smooth Projective Curve

Infinitesimal deformations of some Quot schemes

Irreducibility of Lagrangian Quot schemes over an algebraic curve

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