6 papers · 1 filter
Asymptotic Resurgence of Facet ideals of Graphic Matroids
Michael DiPasquale, Louiza Fouli, Arvind Kumar
Our main results are an upper bound on the asymptotic resurgence of the facet ideal of a graphic matroid in terms of the number of vertices and a lower bound in terms of the circum…
Asymptotic Resurgence of Facet and Stanley-Reisner ideals of Matroids
Michael DiPasquale, Louiza Fouli, Arvind Kumar
Matroid configurations -- introduced by Geramita, Harbourne, Migliore, and Nagel -- are projective varieties which generalize so-called \textit{star configurations} and whose defin…
Resurgence number and convex body associated to pairs of graded families of ideals
Tai Huy Ha, A. V. Jayanthan, Arvind Kumar +1
We discuss how to understand the asymptotic resurgence number of a pair of graded families of ideals from combinatorial data of their associated convex bodies. When the families co…
Generalized Hamming weights and symbolic powers of Stanley-Reisner ideals of matroids
Michael DiPasquale, Louiza Fouli, Arvind Kumar +1
It is well-known that the first generalized Hamming weight of a linear code, more commonly called \textit{the minimum distance} of the linear code, corresponds to the initial degre…
Symbolic Powers of Classical Varieties
Arvind Kumar, Vivek Mukundan
Let and let be homogeneous ideals satisfying certain properties, which include a description of the Noetherian s…
-thresholds of filtrations of ideals
Mitra Koley, Arvind Kumar
In this article, we extend the notion of the -thresholds of ideals to the -thresholds for filtrations of ideals. The existence of -thresholds of filtrations are establishe…