1 citations · 1 across the 10 of their papers we have counts for
15 papers
Epsilon multiplicity, multiplicity=volume formula and analytic spread of family of ideals
Parangama Sarkar
In an analytically unramified local ring of dimension , for a filtration of ideals satisfying co…
-numbers of integral closure filtrations of monomial ideals
Vanmathi A, Parangama Sarkar
In this article, we investigate the -numbers of powers of monomial ideals and their integral closures in a polynomial ring . We provide an alternative proof fo…
Multiplicities of weakly graded families of ideals
Parangama Sarkar
In this article, we extend the notion of multiplicity for weakly graded families of ideals which are bounded below linearly. In particular, we show that the limit $e_W(\mathfrak{I}…
-numbers of symbolic power filtrations
Vanmathi A, Parangama Sarkar
We study the asymptotic behaviour of -number and local -numbers of Noetherian generalized symbolic power filtrations in a Noetherian -graded d…
Epsilon multiplicity and analytic spread of filtrations
Steven Dale Cutkosky, Parangama Sarkar
We extend the epsilon multiplicity of ideals defined by Ulrich and Validashti to epsilon multiplicity of filtrations, and show that under mild assumptions this multiplicity exists…
On a generalized Auslander-Reiten conjecture
Souvik Dey, Shinya Kumashiro, Parangama Sarkar
It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten con…
Analytic Spread of Filtrations and Symbolic Algebras
Steven Dale Cutkosky, Parangama Sarkar
In this paper we define and explore the analytic spread of a filtration in a local ring. We show that, especially for divisorial and symbolic filtrations, some b…
Multiplicities and Mixed Multiplicities of arbitrary Filtrations
Steven Dale Cutkosky, Parangama Sarkar
We develop a theory of multiplicities and mixed multiplicities of filtrations, extending the theory for filtrations of -primary ideals to arbitrary (not necessarily Noetherian)…
Frobenius Betti numbers and syzygies of finite length modules
Ian M. Aberbach, Parangama Sarkar
Let be a local (Noetherian) ring of dimension and a finite length -module with free resolution . De Stefani, Huneke, and Núñez-Betancourt ex…
Mixed Multiplicities of Filtrations
Steven Dale Cutkosky, Parangama Sarkar, Hema Srinivasan
In this paper we define and explore properties of mixed multiplicities of (not necessarily Noetherian) filtrations of -primary ideals in a Noetherian local ring , generaliz…
Rees' theorem for filtrations, multiplicity function and reduction criteria
Parangama Sarkar
Let be ideals in a formally equidimensional local ring with Rees proved that for all , is a polynomial in of degre…
Multigraded regularity, reduction vectors and postulation vectors
Parangama Sarkar
We relate the set of complete reduction vectors of a -graded admissible filtration of ideals with the set of multigraded regularities of $G(\mathcal{F})…
Variations on the Grothendieck-Serre Formula for Hilbert functions and their applications
Shreedevi K. Masuti, Parangama Sarkar, J. K. Verma
In this expository paper we present proofs of Grothendieck-Serre Formula for multi-graded algebras and Rees algebras for admissible multi-graded filtrations. As applications, we de…
Postulation and reduction vectors of multigraded filtrations of ideals
Parangama Sarkar, J. K. Verma
We study relationship between postulation and reduction vectors of admissible multigraded filtrations of id…
Local cohomology of multi-Rees algebras, Joint reduction numbers and product of complete ideals
Parangama Sarkar, J. K. Verma
We find conditions on the local cohomology modules of multi-Rees algebras of admissible filtrations which enable us to predict joint reduction numbers. As a consequence we are able…