A note on the regularity of products

2010/05/25 by Seyed Hamid Hassanzadeh, Hassanzadeh, Seyed Hamid, Yassemi, Siamak
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.1005.4638

openalex publication_date 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S=\Bbb K[x₁,…,x_n] denote a polynomial ring over a field \Bbb K. Given a monomial ideal I and a finitely generated multigraded M over S, we follow Herzog's method to construct a multigraded free S-resolution of M/IM by using multigraded S-free resolutions of S/I and M. The complex constructed in this paper is used to prove the inequality \Reg(IM)≤ \Reg(I)+\Reg(M) for a large class of ideals and modules. In the case where M is an ideal, under one relative condition on the generators which specially does not involve the dimensions, the inequality \Reg(IM)≤ \Reg(I)+\Reg(M) is proven.

Citations

• Characteristic-free bounds for the Castelnuovo–Mumford regularity
• Castelnuovo-Mumford regularity of products of ideals

Related

• Castelnuovo-Mumford regularity of products of ideals
• The regularity of monomial ideals and their integral closures
• Minimal free resolutions and asymptotic behavior of multigraded regularity
• Regularity of S_n-invariant monomial ideals
• The Herzog-Takayama resolution over a skew polynomial ring