Critical binomial ideals of Norhtcott type

2017/05/29 by P. A. García-Sánchez, Pedro A. García-Sánchez, D. Llena +5
Computer Science · Mathematics · #13F20 (Primary) 13C40 #16W50 (Secondary) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13C40 #msc:13F20 #msc:16W50

paper · pdf · doi:10.48550/arxiv.1705.10268

arxiv created 2017/05/29 · openalex publication_date 2017/05/29 · arxiv updated 2017/05/30 · openalex created_date 2017/06/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a family of binomial ideals defining monomial curves in the n-dimensional affine space determined by n hypersurfaces of the form x_i^c_i - x₁^u_i1 ⋯ x_n^u_1n ∈ k[x₁, …, x_n] with u_ii = 0, i∈ \ 1, …, n\. We prove that, the monomial curves in that family are set-theoretic complete intersection. Moreover, if the monomial curve is irreducible, we compute some invariants such as genus, type and Fröbenius number of the corresponding numerical semigroup. We also describe a method to produce set-theoretic complete intersection semigroup ideals of arbitrary large height.

Related

• The primary components of positive critical binomial ideals
• Producing Set Theoretic Complete Intersection Monomial Curves in Pⁿ
• On the Rich Landscape of Complete Intersection Monomial Curves
• Ideals of Herzog-Northcott type
• Betti numbers of the tangent cones of monomial space curves