Ronnie Sebastian

activity

20092026

most citedFundamental Group Schemes of Hilbert Scheme of

n

Points on a Smooth Projective Surface

4 citations · 7 across the 13 of their papers we have counts for

collaborators

19 papers

math.AC2026

On the variety of sum of powers of certain complete intersection forms

Meghana Bhat, Ronnie Sebastian

Let $F$ be a homogeneous polynomial (form). If the annihilator ideal $F^{⊥}$ is a complete intersection, then $F$ is called as a complete intersection form. For many complete int…

math.AC2026

Waring rank of certain complete intersection forms

Meghana Bhat, Enrico Carlini, Shreedevi K. Masuti +1

The complete intersection forms are the homogeneous polynomials whose annihilator ideal or the Macaulay dual, is an Artinian complete intersection ideal. In this paper, we compute…

math.AG2025

Some recent results on the punctual Quot schemes

Indranil Biswas, Chandranandan Gangopadhyay, Ronnie Sebastian

Let $C$ be a smooth projective curve defined over the field of complex numbers. Let $E$ be a vector bundle on $C$ , and fix an integer $d ⩾ 1$ . Let $\mc Q:={\rm Quot}(E,d)$ b…

math.AG2024

Infinitesimal deformations of some quot schemes, II

Indranil Biswas, Chandranandan Gangopadhyay, Ronnie Sebastian

Let $C$ be an irreducible smooth complex projective curve of genus $g$ , with $g_{C} ⩾ 2$ . Let $E$ be a vector bundle on $C$ of rank $r$ , with $r ⩾ 2$ . Let $\mc Q:=\mc…

math.AG2024

Nef and Effective cones of some Quot Schemes

Chandranandan Gangopadhyay, Ronnie Sebastian

Let $C$ be a smooth projective curve over $C$ of genus $g (C) ⩾ 3$ (respectively, $g (C) = 2$ ). Fix integers $r, k$ such that $2 ⩽ k ⩽ r - 2$ , (respectively,…

math.AG2024

Irreducibility and singularities of some nested Quot schemes

Parvez Rasul, Ronnie Sebastian

Let $C$ be a smooth projective curve over $C$ of genus $g ⩾ 1$ . Let $E$ be a vector bundle on $C$ of rank $r$ and degree $e$ . Given integers $k_{1}, k_{2}, d_{1}, d_{2}$ such t…

math.AG2022

Picard Groups of Some Quot Schemes

Chandranandan Gangopadhyay, Ronnie Sebastian

Let $C$ be a smooth projective curve over the field of complex numbers $C$ of genus $g (C) > 0$ . Let $E$ be a locally free sheaf on $C$ of rank $r$ and degree $e$ . Let $\math…

math.AG2022★ 1 cited

Irreducibility of Some Nested Hilbert Schemes

Chandranandan Gangopadhyay, Parvez Rasul, Ronnie Sebastian

Let $S$ be a smooth projective surface over $C$ . Let $S^{[n_{1}, \dots, n_{k}]}$ denote the nested Hilbert scheme which parametrizes zero-dimensional subschemes $ξ_{n_1} \subset…

math.AG2022

Infinitesimal deformations of some Quot schemes

Indranil Biswas, Chandranandan Gangopadhyay, Ronnie Sebastian

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…

math.AG2021

Seshadri constants on some Quot schemes

Chandranandan Gangopadhyay, Krishna Hanumanthu, Ronnie Sebastian

Let $E$ be a vector bundle of rank $n$ on $P^{1}$ . Fix a positive integer $d$ . Let $Q (E, d)$ denote the Quot scheme of torsion quotients of $E$ of degree $d$ and le…

math.AG2020

Rank 2 Ulrich bundles on general double plane covers

Ronnie Sebastian, Amit Tripathi

We prove that a double cover of $P^{2}$ ramified along a general smooth curve B of degree $2 s$ , for $s \geq 3$ , supports a rank 2 special Ulrich bundle.

math.AG2020

Nef cones of some Quot schemes on a smooth projective curve

Chandranandan Gangopadhyay, Ronnie Sebastian

Let $C$ be a smooth projective curve over $C$ . Let $n, d \geq 1$ . Let $Q$ be the Quot scheme parameterizing torsion quotients of the vector bundle $O_{C}^{n}$ o…

math.AG2019

Fundamental Group Schemes of some Quot Schemes on a smooth projective curve

Chandranandan Gangopadhyay, Ronnie Sebastian

Let $k$ be an algebraically closed field. Let $C$ be an irreducible smooth projective curve over $k$ . Let $E$ be a locally free sheaf on $C$ of rank $\geq 2$ . Fix an integer $d \ge…

math.AG2019

Fundamental Group Schemes of $n$ -fold Symmetric Product of a Smooth Projective Curve

Arjun Paul, Ronnie Sebastian

Let $k$ be an algebraically closed field of characteristic $p > 0$ . Let $X$ be an irreducible smooth projective curve of genus $g$ over $k$ . Fix an integer $n \geq 2$ , and let $S^n…

math.AG2019★ 4 cited

Fundamental Group Schemes of Hilbert Scheme of $n$ Points on a Smooth Projective Surface

Arjun Paul, Ronnie Sebastian

Let $k$ be an algebraically closed field of characteristic $p > 3$ . Let $X$ be an irreducible smooth projective surface over $k$ . Fix an integer $n \geq 1$ and let ${\mathcal{H}{\i…

math.AG2018

Rationality of moduli spaces of stable bundles on curves over $R$

Souradeep Majumder, Ronnie Sebastian

Let $C$ be a smooth, projective, geometrically irreducible curve defined over $R$ such that $C (R) = \emptyset$ . Let $r > 0$ and $d$ be integers which are coprime. L…

math.AG2014★ 1 cited

Smash nilpotence on uniruled 3-folds

Ronnie Sebastian

Voevodsky has conjectured that numerical and smash equivalence coincide on a smooth projective variety. We prove this conjecture holds for uniruled 3-folds and for one dimensional…

math.AG2012★ 1 cited

Smash nilpotent cycles on products of curves

Ronnie Sebastian

Voevodsky has conjectured that numerical and smash equivalence coincide on a smooth projective variety. We prove the conjecture for one dimensional cycles on an arbitrary product o…

math.AG2009

Smash-nilpotent cycles on abelian 3-folds

Bruno Kahn, Ronnie Sebastian

We show that homologically trivial algebraic cycles on a 3-dimensional abelian variety are smash-nilpotent.

On the variety of sum of powers of certain complete intersection forms

Waring rank of certain complete intersection forms

Some recent results on the punctual Quot schemes

Infinitesimal deformations of some quot schemes, II

Nef and Effective cones of some Quot Schemes

Irreducibility and singularities of some nested Quot schemes

Picard Groups of Some Quot Schemes

Irreducibility of Some Nested Hilbert Schemes

Infinitesimal deformations of some Quot schemes

Seshadri constants on some Quot schemes

Rank 2 Ulrich bundles on general double plane covers

Nef cones of some Quot schemes on a smooth projective curve

Fundamental Group Schemes of some Quot Schemes on a smooth projective curve

Fundamental Group Schemes of n-fold Symmetric Product of a Smooth Projective Curve

Fundamental Group Schemes of Hilbert Scheme of n Points on a Smooth Projective Surface

Rationality of moduli spaces of stable bundles on curves over R

Smash nilpotence on uniruled 3-folds

Smash nilpotent cycles on products of curves

Smash-nilpotent cycles on abelian 3-folds

Fundamental Group Schemes of $n$ -fold Symmetric Product of a Smooth Projective Curve

Fundamental Group Schemes of Hilbert Scheme of $n$ Points on a Smooth Projective Surface

Rationality of moduli spaces of stable bundles on curves over $R$