On Regular Sequences in the Form Module with Applications to Local Bézout Inequalities

2017/05/11 by Khadam, M. Azeem
#Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13H15 #Secondary: 13D40

paper · doi:10.48550/arxiv.1705.04024

Abstract

Let \mathfrakq denote an ideal in a Noetherian local ring (A,\mathfrakm). Let \underlinea=a₁,…,a_d ⊂ \mathfrakq denote a system of parameters in a finitely generated A-module M. This note investigate an improvement of the inequality c₁⋅ … ⋅ c_d ⋅ e₀(\mathfrakq;M) ≤ ℓ_A(M/\underlinea M), where c_i denote the initial degrees of a_i in the form ring G_A(\mathfrakq). To this end, there is an investigation of regular sequences in the form module G_M(\mathfrakq) by homology of a factor complex of the Koszul complex. In a particular case, there is a discussion of classical local Bézout inequality in the affine d-space \mathbbA^d_k.

Related

• Local Bezout estimates and multiplicities of parameter and primary\n ideals
• Regular sequences and local cohomology modules with respect to a pair of ideals
• Lech's inequality, the Stückrad--Vogel conjecture, and uniform behavior of Koszul homology
• Koszul cohomology and support of local cohomology modules of complete intersections
• On the Stability of Bass and Betti Numbers under Ideal Perturbations in a Local Ring