2024/03/27 by Giuseppe Zappalà, Zappalà, Giuseppe
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2403.18507
openalex publication_date 2024/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Hilbert function and the graded Betti numbers of almost complete intersection artinian algebras. We show that that every Hilbert function of a complete intersection artinian algebra is the Hilbert function of an almost complete intersection algebra. In codimension 3 we focus on almost complete intersection artinian algebras whose Hilbert function coincides with that of a complete intersection defined by 3 forms of the same degree. We classify all the possible graded Betti numbers of such algebras and we specify what cancellations are allowed in a minimal graded free resolution.