My research interest lie in Commutative Algebra and Algebraic Geometry related areas. We study about various homological properties namely depth, Cohen-Macaulayness, Castelnuovo-Mumford regularity, Gorensteinness and relation type of blowup algebras, namely, the Rees algebra, the associated graded ring and a special fiber known as fiber cone. The notion blowup algebras refers to certain algebraic objects associated with the process of blowing up a variety along a subvariety, introduced by Hironaka. Also we study about the Hilbert coefficients of Schubert varieties in Grassmannians. Recently, we are studying about the syzygies of Koszul algebras and their homological properties.
Syzygies , Deformations of Koszul Algebras and Regularity of Modules Over Them NATIONAL BOARD OF HIGHER MATHEMATICS(NBHM)
Koszul Algebras ISIRD, SRIC
Area of Research: Commutative Algebra
Rahul Singh Karki
Area of Research: