Algebraic Geometry; Combinatorial
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),
- (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, .