Subject Area: Algebraic Geometry; Combinatorial Commutative Algebra

My research interest in algebraic geometry includes study of moduli space of vector bundles, Geometric Invariant Theory and Classical Algebraic Geometry.

For the last five years, I have been interested in some aspects of Combinatorial Commutative Algebra; namely, the study of free resolutions of monomial ideals, computation of their Betti numbers and relationship between their combinatorial and algebraic properties.

- Invariant vector bundles of rank-2 on hyperelliptic curves, Michigan Math.J. 47 (2000), 575-584.
- Linear systems and quotients of Projective space, Bulletin London Math. Soc. 35 (2003), 152-160.
- (with P. Singh and A. Kumar), Nearly extremal Cohen-Macaulay and Gorenstein Algebras, Bulletin Australian Math. Soc. 75 (2007), 211-219.
- (with P. Singh), Deficiently extremal Cohen-Macaulay Algebras, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 120, No. 2, April 2010.
- (with I. Biswas and Y. I. Holla), On Moduli spaces of Parabolic Vector bundles of rank 2 over Complex projective line, Michigan Math. J. Vol. 59 (2010), 467-479, .