On the h-vectors of the powers of graded ideals

2017/04/19 by Seyed Shahab Arkian, Амир Мафи, Arkian, Seyed Shahab +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1704.05601

openalex publication_date 2017/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S=K[x₁,…,x_n] be the polynomial ring over the field K, and let I⊂ S be a graded ideal. It is shown that for k ≫0 the postulation number of I^k is bounded by a linear function of k, and it is a linear function of k, if I is generated in a single degree. By using the relationship of the h-vector with the higher iterated Hilbert coefficients of I^k it is shown that the Hilbert coefficients e_i(I^k) of I^k are polynomials for k ≫ 0, whenever I is generated in a single degree.

Related

• The saturation number of powers of graded ideals
• Asymptotic behaviour of the v-number of homogeneous ideals
• Lexsegment ideals and their h-polynomials
• Higher iterated Hilbert coefficients of the graded components of bigraded modules
• Powers are Golod