Periodic Occurance of Complete Intersection Monomial Curves

2012/03/09 by A. V. Jayanthan, Jayanthan, A. V., Hema Srinivasan +1
Computer Science · Mathematics · #13C40 #14H50 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis #math.AC #math.AG #msc:13C40 #msc:14H50

paper · pdf · doi:10.48550/arxiv.1203.1991

12 pages, added a reference which was missing in the earlier version

openalex publication_date 2012/03/09 · arxiv created 2012/03/19 · arxiv updated 2012/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the complete intersection property of monomial curves in the family Γ_{å+ \jj} = (t^{a₀ + j}, t^a₁+j,..., t^{a_n + j}) ~ | ~ j ≥ 0, ~ a₀ < a₁ <...< a_n. We prove that if Γ_å+\jj is a complete intersection for j ≫0, then Γ_å+\jj+\underlinea_n is a complete intersection for j ≫ 0. This proves a conjecture of Herzog and Srinivasan on eventual periodicity of Betti numbers of semigroup rings under translations for complete intersections. We also show that if Γ_å+\jj is a complete intersection for j ≫ 0, then Γ_å is a complete intersection. We also characterize the complete intersection property of this family when n = 3.

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