2025/06/10 by A Vanmathi, A, Vanmathi, Parangama Sarkar +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2506.09051
openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we investigate the v-numbers of powers of monomial ideals and their integral closures in a polynomial ring S. We provide an alternative proof for determining the v-numbers of powers of complete intersection monomial ideals. Furthermore, we analyze the v-numbers associated to integral closure filtrations of irreducible monomial ideals and explore their relationship with the Castelnuovo-Mumford regularity of these ideals. Consequently, we obtain that for all n≥ 1, reg(S/In)=v(In)=nα(I)-1 where I is an equigenerated irreducible monomial ideal. Finally, we give an upper bound for v-numbers associated to the integral closure filtrations of complete intersection monomial ideals and explicitly compute these v-numbers in certain cases. As a consequence, we show that for any integer a≥ 1, there exists a height two equigenerated complete intersection monomial ideal I such that reg(S/In)-v(In)=a-1 for all n≥ 1. Moreover, we establish that for complete intersection monomial ideals, the v-numbers of powers of ideals can be arbitrarily larger than the v-numbers of integral closures of their powers.