Chanchal Kumar

PIC

Subject Area: Algebraic Geometry; Combinatorial Commutative Algebra

Background and Research Interests

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.

Select Publications

  1. Invariant vector bundles of rank-2 on hyperelliptic curves, Michigan Math.J. 47 (2000), 575-584.
  2. Linear systems and quotients of Projective space, Bulletin London Math. Soc. 35 (2003), 152-160.
  3. (with P. Singh and A. Kumar), Nearly extremal Cohen-Macaulay and Gorenstein Algebras, Bulletin Australian Math. Soc. 75 (2007), 211-219.
  4. (with P. Singh), Deficiently extremal Cohen-Macaulay Algebras, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 120, No. 2, April 2010.
  5. (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, .