The first Hilbert coefficient of stretched ideals

2021/12/04 by Kazuho Ozeki, Ozeki, Kazuho
Mathematics · #13D40 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13A30 #Secondary: 13H10 #math.AC #msc:13A30 #msc:13D40 #msc:13H10

paper · pdf · doi:10.48550/arxiv.2112.02294

17 pages. arXiv admin note: substantial text overlap with arXiv:2109.12918

arxiv created 2021/12/04 · arxiv updated 2021/12/07

Abstract

In this paper we explore the almost Cohen-Macaulayness of the associated graded ring of stretched \mathfrakm-primary ideals with small first Hilbert coefficient in a Cohen-Macaulay local ring (A,\mathfrakm). In particular, we explore the structure of stretched \mathfrakm-primary ideals satisfying the equality e₁(I)=e₀(I)-ℓ_A(A/I)+4 where e₀(I) and e₁(I) denote the multiplicity and the first Hilbert coefficient respectively.

Citations

• The reduction number of stretched ideals

Related

• The reduction number of stretched ideals
• Hilbert Coefficients and Depth of the Associated Graded Ring of an Ideal
• Bounds for the first Hilbert coefficients of \mathfrak m-primary ideals
• The second Hilbert coefficients and the sectional genera of ideals
• Depth of associated graded rings via Hilbert coefficients of ideals