8 papers
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…
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…
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…