Ronnie Sebastian
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Ronnie Sebastian has a total of 14 co-authors. Here are the top co-authors by number of shared publications:
- Chandranandan Gangopadhyay
Shiv Nadar University, Greater Noida, India
6 shared publications - Arjun Paul
Tata Institute of Fundamental Research
4 shared publications Chandranandan Gangopadhyay
Department of Mathematics, Indian Institute of Science Education and Research , Pune, 411008, Maharashtra, India
2 shared publications- Chandranandan Gangopadhyay
Department of Mathematics, Indian Institute of Science Education and Research, Pune, India
2 shared publications - Indranil Biswas
Department of Mathematics, Shiv Nadar University, Greater Noida, India
2 shared publications - Krishna Hanumanthu
Chennai Mathematical Institute, Kelambakkam, India
2 shared publications
Latest Publications
- 3 June 2026
- Published by Springer Nature
- p. 21-55
Some Recent Results on the Punctual Quot Schemes
- 6 May 2026
- Published by Springer Nature in manuscripta mathematica
- Vol. 177 (3) , 36
Seshadri constants and negative curves on blowups of ruled surfaces
- 6 May 2026
- Published by Springer Nature in manuscripta mathematica
- Vol. 177 (3) , 36
Seshadri constants and negative curves on blowups of ruled surfaces
- 5 March 2024
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2024 (9) , 8067-8100
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 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].- 5 March 2024
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2024 (9) , 8067-8100
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 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].- Open Access
Picard Groups of Some Quot Schemes
Let $C$ be a smooth projective curve over the field of complex numbers $\mathbb{C}$ of genus $g(C)>0$. Let $E$ be a locally free sheaf on $C$ of rank $r$ and degree $e$. Let $\mathcal{Q}:={\rm Quot}_{C/\mathbb{C}}(E,k,d)$ denote the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. For $k>0$ and $d\gg 0$ we compute the Picard group of $\mathcal{Q}$.Open AccessPicard Groups of Some Quot Schemes
Let $C$ be a smooth projective curve over the field of complex numbers $\mathbb{C}$ of genus $g(C)>0$. Let $E$ be a locally free sheaf on $C$ of rank $r$ and degree $e$. Let $\mathcal{Q}:={\rm Quot}_{C/\mathbb{C}}(E,k,d)$ denote the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. For $k>0$ and $d\gg 0$ we compute the Picard group of $\mathcal{Q}$. - 23 February 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 152 (05) , 1857-1870
Irreducibility of some nested Hilbert schemes
Let S S be a smooth projective surface over C \mathbb {C} . Let S [ n 1 , … , n k ] S^{[n_1,\dots ,n_k]} denote the nested Hilbert scheme which parametrizes zero-dimensional subschemes ξ n 1 ⊂ … ⊂ ξ n k \xi _{n_1} \subset \ldots \subset \xi _{n_k} where ξ i \xi _i is a closed subscheme of S S of length i i . We show that S [ n , m ] S^{[n,m]} , S [ n , m , m + 1 ] S^{[n,m,m+1]} , S [ n , n + 1 , m ] S^{[n,n+1,m]} , S [ n , n + 1 , m , m + 1 ] S^{[n,n+1,m,m+1]} , S [ n , n + 2 , m ] S^{[n,n+2,m]} and S [ n , n + 2 , m , m + 1 ] S^{[n,n+2,m,m+1]} are irreducible.
- 23 February 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 152 (05) , 1857-1870
Irreducibility of some nested Hilbert schemes
Let S S be a smooth projective surface over C \mathbb {C} . Let S [ n 1 , … , n k ] S^{[n_1,\dots ,n_k]} denote the nested Hilbert scheme which parametrizes zero-dimensional subschemes ξ n 1 ⊂ … ⊂ ξ n k \xi _{n_1} \subset \ldots \subset \xi _{n_k} where ξ i \xi _i is a closed subscheme of S S of length i i . We show that S [ n , m ] S^{[n,m]} , S [ n , m , m + 1 ] S^{[n,m,m+1]} , S [ n , n + 1 , m ] S^{[n,n+1,m]} , S [ n , n + 1 , m , m + 1 ] S^{[n,n+1,m,m+1]} , S [ n , n + 2 , m ] S^{[n,n+2,m]} and S [ n , n + 2 , m , m + 1 ] S^{[n,n+2,m,m+1]} are irreducible.
- 22 February 2024
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2024 (11) , 9194-9217
Picard Groups of Some Quot Schemes
Let $C$ be a smooth projective curve over the field of complex numbers ${\mathbb{C}}$ of genus $g(C)>0$. Let $E$ be a locally free sheaf on $C$ of rank $r$ and degree $e$. Let $\mathcal{Q}:=\textrm{Quot}_{C/{\mathbb{C}}}(E,k,d)$ denote the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. For $k>0$ and $d\gg 0$, we compute the Picard group of $\mathcal{Q}$.- 22 February 2024
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2024 (11) , 9194-9217
Picard Groups of Some Quot Schemes
Let $C$ be a smooth projective curve over the field of complex numbers ${\mathbb{C}}$ of genus $g(C)>0$. Let $E$ be a locally free sheaf on $C$ of rank $r$ and degree $e$. Let $\mathcal{Q}:=\textrm{Quot}_{C/{\mathbb{C}}}(E,k,d)$ denote the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. For $k>0$ and $d\gg 0$, we compute the Picard group of $\mathcal{Q}$.- Open Access
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 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 $\mathcal{Q}(E,d)$.Open AccessInfinitesimal 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 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 $\mathcal{Q}(E,d)$. - Open Access
Irreducibility of Some Nested Hilbert Schemes
Let $S$ be a smooth projective surface over $\mathbb{C}$. Let $S^{[n_1,\dots,n_k]}$ denote the nested Hilbert scheme which parametrizes zero-dimensional subschemes $\xi_{n_1} \subset \ldots \subset \xi_{n_k}$ where $\xi_i$ is a closed subscheme of $S$ of length $i$. We show that $S^{[n,m]}$, $S^{[n,m,m+1]}$, $S^{[n,n+1,m]}$, $S^{[n,n+1,m,m+1]}$, $S^{[n,n+2,m]}$ and $S^{[n,n+2,m,m+1]}$ are irreducible.Open AccessIrreducibility of Some Nested Hilbert Schemes
Let $S$ be a smooth projective surface over $\mathbb{C}$. Let $S^{[n_1,\dots,n_k]}$ denote the nested Hilbert scheme which parametrizes zero-dimensional subschemes $\xi_{n_1} \subset \ldots \subset \xi_{n_k}$ where $\xi_i$ is a closed subscheme of $S$ of length $i$. We show that $S^{[n,m]}$, $S^{[n,m,m+1]}$, $S^{[n,n+1,m]}$, $S^{[n,n+1,m,m+1]}$, $S^{[n,n+2,m]}$ and $S^{[n,n+2,m,m+1]}$ are irreducible. - Open Access
Seshadri constants on some Quot schemes
Let $E$ be a vector bundle of rank $n$ on $\mathbb{P}^1$. Fix a positive integer $d$. Let $\mathcal{Q}(E,d)$ denote the Quot scheme of torsion quotients of $E$ of degree $d$ and let $Gr(E,d)$ denote the Grassmann bundle that parametrizes the $d$-dimensional quotients of the fibers of $E$. We compute Seshadri constants of ample line bundles on $\mathcal{Q}(E,d)$ and $Gr(E,d)$.Open AccessSeshadri constants on some Quot schemes
Let $E$ be a vector bundle of rank $n$ on $\mathbb{P}^1$. Fix a positive integer $d$. Let $\mathcal{Q}(E,d)$ denote the Quot scheme of torsion quotients of $E$ of degree $d$ and let $Gr(E,d)$ denote the Grassmann bundle that parametrizes the $d$-dimensional quotients of the fibers of $E$. We compute Seshadri constants of ample line bundles on $\mathcal{Q}(E,d)$ and $Gr(E,d)$. - 1 October 2021
- Published by Springer Nature in Proceedings - Mathematical Sciences
- Vol. 131 (2) , 1-10
Fundamental group schemes of n-fold symmetric product of a smooth projective curve
- 1 October 2021
- Published by Springer Nature in Proceedings - Mathematical Sciences
- Vol. 131 (2) , 1-10
Fundamental group schemes of n-fold symmetric product of a smooth projective curve