12 citations · 12 across the 11 of their papers we have counts for
12 papers
Lie's classification of finite dimensional algebras of Vector Fields in C^N
Hassan Azad, Indranil Biswas, Said Waqas Shah
Brief proofs of classical results of Lie on finite dimensional subalgebras of vector fields in two and three variables are outlined. The results for algebras of maximal rank for ve…
Positivity of Higgs Vector Bundles
Indranil Biswas, Snehajit Misra, Nabanita Ray
In \cite{BCO25}, Bruzzo, Capasso and Otero extended the notion of ampleness of vector bundles to the more general context of Higgs bundles. But the ampleness of Higgs bundles did n…
Nilpotent Lie algebras of vector fields in three variables
Hassan Azad, Indranil Biswas, Ryad Ghanam
We give a complete constructive description of all finite dimensional nilpotent Lie algebras of smooth vector fields in three variables, including intransitive algebras. The descri…
Isomorphisms between moduli stacks of vector bundles with fixed determinant
David Alfaya, Indranil Biswas, Tomás L. Gómez
We classify all isomorphisms between moduli stacks of vector bundles of fixed determinant on a smooth complex projective of genus at least 4. It is shown that each isomorphism betw…
On Lie's classification of nonsolvable subalgebras of vector fields on the plane
Hassan Azad, Indranil Biswas, Ahsan Fazil +1
A brief proof of Lie's classification of finite dimensional subalgebras of vector fields on the complex plane that have a proper Levi decomposition is given. The proof uses basic r…
Remarks on Higgs bundles twisted by a vector bundle
David Alfaya, Indranil Biswas, Pradip Kumar
For any V-twisted Higgs bundle on a compact Riemann surface X, where V is a holomorphic vector bundle of rank two on X, there are two associated Higgs bundles on X, twisted by line…
Anti-ample bundle, nef vector bundle, big vector bundle
Indranil Biswas, Fatima Laytimi, D. S. Nagaraj +1
We prove that the direct image of an anti-ample vector bundle is anti-ample under any finite flat morphism of non-singular projective varieties. In the second part we prove some pr…
Equivariant vector bundles over the complex projective line
Indranil Biswas, Francois-Xavier Machu
Let be a finite abelian group acting faithfully on via holomorphic automorphisms. In \cite{DF2} the --equivariant algebraic vector bundles on -…
Semisimple Algebras of Vector Fields on
Sajid Ali, Hassan Azad, Indranil Biswas +2
A local classification of semisimple algebras of vector fields on is given, using the canonical forms of the Heisenberg algebra and of $sl(2,\mathbb{C})\times sl(2…
Torelli theorem for moduli stacks of vector bundles and principal G-bundles
David Alfaya, Indranil Biswas, Tomás L. Gómez +1
Given any irreducible smooth complex projective curve , of genus at least , consider the moduli stack of vector bundles on of fixed rank and determinant. It is proved tha…
Semisimple algebras of vector fields on C^N of maximal rank
Hassan Azad, Indranil Biswas, Fazal M. Mahomed
A classification of semisimple algebras of vector fields on C^N that have a Cartan subalgebra of dimension N is given. The proof uses basic representation theory and the local cano…
On computing joint invariants of vector fields
H. Azad, I. Biswas, R. Ghanam +1
A constructive version of the Frobenius integrability theorem -- that can be programmed effectively -- is given. This is used in computing invariants of groups of low ranks and rec…