On the resurgence and asymptotic resurgence of homogeneous ideals

2021/06/29 by A. V. Jayanthan, Arvind Kumar, Jayanthan, A. V. +3 · 3 citations
Computer Science · Mathematics · #05E40 #13A15 #13F20 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2106.15261

openalex publication_date 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbbK be a field and R = \mathbbK[x₁, …, x_n]. We obtain an improved upper bound for asymptotic resurgence of squarefree monomial ideals in R. We study the effect on the resurgence when sum, product and intersection of ideals are taken. We obtain sharp upper and lower bounds for the resurgence and asymptotic resurgence of cover ideals of finite simple graphs in terms of associated combinatorial invariants. We also explicitly compute the resurgence and asymptotic resurgence of cover ideals of several classes of graphs. We characterize a graph being bipartite in terms of the resurgence and asymptotic resurgence of edge and cover ideals. We also compute explicitly the resurgence and asymptotic resurgence of edge ideals of some classes of graphs.

Cited by

• Waldschmidt constant of monomial ideals and Simis ideals
• Graded families of ideals and convex regions
• Asymptotic Resurgence of Facet ideals of Graphic Matroids

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