Publications

A note on parabolic bundles over nodal curves (with Sanjay Singh) Int. J. Math. 33 (2022), no. 3

Mehta and Seshadri proved that the set of equivalence classes of irreducible unitary representations of the fundamental group of a punctured compact Riemann surface, can be identified with the set of equivalence classes of stable parabolic bundles of parabolic degree zero on the compact Riemann surface. In this paper, we discuss the Mehta–Seshadri correspondence over an irreducible projective curve with at most nodes as singularities.

Projective Poincaré and Picard bundles for moduli spaces of vector bundles over nodal curves (with Usha N. Bhosle and Sanjay Singh) Bull. Sci. Math. 166 (2021)

We discuss the non-existence of a Poincaré bundle parametrised by the moduli space of vector bundles on nodal curves when the rank and degree are not coprime. Although the existence of Poincaré bundles (hence Picard bundles) depend on the rank and degree being relatively prime, there always exists a Poincaré family of projective bundles parametrised by the open subset of stable bundles, called the projective Poincaré bundle. Similarly, there is a projective Picard bundle. We prove the stability of these bundles under suitable polarisations. On the way to achieve these goals, we compute the codimension of a few closed subsets of the moduli spaces. They are of independent interest and have other applications; we discuss a few of them.

A note on generalized derivations as Jordan homomorphisms (with Shailesh Kumar Tiwari) Bull. Korean Math. Soc. 57 (2020), no. 3, p. 709–737

On a prime ring with characteristic different from 2, we characteirse and give complete descriptions of generalised derivations satisfying a fixed polynomial identity. 

In Preparation

Minimal rational curves in the moduli spaces of stable vector bundles on nodal curves 

Stability of the parabolic Picard bundle