14 papers
Tangent bundles of Quot schemes of vector bundles on curves
Ashima Bansal, Supravat Sarkar, Shivam Vats
For a vector bundle on a smooth projective curve , one defines the Quot scheme parametrizing subsheaves of having length torsion quotients. We describe…
Torelli theorems for Quot schemes of vector bundles on curves
Ashima Bansal, Supravat Sarkar, Shivam Vats
For a vector bundle on a smooth projective curve , one defines the Quot scheme parametrizing subsheaves of having length torsion quotients. If is a…
Positive Cones of Parabolic Grassmann Bundle over a curve
Ashima Bansal, Shivam Vats
In this article, we define the parabolic Grassmann bundle associated to a parabolic vector bundle over a smooth projective variety, generalizing the construction of parabolic proje…
On positive cones of finite quotients of a normal variety
Ashima Bansal, Indranil Biswas, Souradeep Majumder
We study positivity properties of finite flat quotients of normal projective varieties. We show that the numerical groups and positive cones of these quotient varieties are related…
A criterion for parabolic vector bundles to admit a parabolic Lie algebroid connection
David Alfaya, Ashima Bansal, Indranil Biswas +1
Given a holomorphic Lie algebroid on a compact connected Riemann surface , we give a necessary and sufficient condition for a parabolic vector bundle on , with parab…
Singularity of cubic hypersurfaces and hyperplane sections of projectivized tangent bundle of projective space
Ashima Bansal, Supravat Sarkar, Shivam Vats
We show that the normal points of a cubic hypersurface in projective space have canonical singularities unless the hypersurface is an iterated cone over an elliptic curve. As an ap…
Lie algebroid connection and Harder-Narasimhan reduction
Ashima Bansal, Indranil Biswas, Pradip Kumar
Take a holomorphic Lie algebroid on a compact connected Riemann surface such that the anchor map is not surjective. Let be a parabolic subgroup of a complex…
Pullback and Direct Image of Parabolic Ample and Parabolic Nef Vector Bundles
Ashima Bansal, Indranil Biswas
We prove that under a finite surjective map of irreducible smooth complex projective curves, the pullback and direct image of a parabolic ample (respectively, parabolic nef) vector…
Automorphisms of punctual Hilbert schemes and symmetric powers of varieties
Ashima Bansal, Supravat Sarkar, Shivam Vats
We classify complex smooth projective surfaces whose punctual Hilbert scheme has a non-natural automorphism preserving the big diagonal. This completely answers a question raised b…
Isomorphisms and automorphisms of multiprojective bundles and symmetric powers of projective bundles
Ashima Bansal, Supravat Sarkar, Shivam Vats
We describe when two multiprojective bundles (fibre products of projective bundles over the same base) over projective spaces are isomorphic as abstract varieties. We also describe…
Symmetric power of higher dimensional varieties
Ashima Bansal, Supravat Sarkar, Shivam Vats
We study several properties of the symmetric power of a smooth variety . We describe the Picard and divisor class groups of when is projective. We give a compl…
Positive Cones of the Projectivization of a parabolic vector bundle and Their Products over a Curve
Ashima Bansal, Indranil Biswas, Souradeep Majumder
We compute the positive cones of the projectivization of a parabolic vector bundle and the fiber product of two parabolic projective bundles over a smooth complex projective curve.…
Extremal Contraction of Projective Bundles
Ashima Bansal, Supravat Sarkar, Shivam Vats
In this article, we explore the extremal contractions of several projective bundles over smooth Fano varieties of Picard rank . We provide a whole class of examples of projectiv…
Isomorphism of Multiprojective Bundles and Projective Towers
Ashima Bansal, Supravat Sarkar, Shivam Vats
We study when two projective bundles over two arbitrary smooth projective varieties of different dimensions can be isomorphic. We show that two multi-projective bundles (fibre prod…