A Structure Theorem and the Graded Betti Numbers for Almost Complete Intersections

2010/02/16 by Alfio Ragusa, Ragusa, Alfio, Giuseppe Zappalà +1
Computer Science · Mathematics · #13D40 #13H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1002.3026

openalex publication_date 2010/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a structure theorem for all almost complete intersection ideals of depth three in any Noetherian local ring. In particular, we find that the minimal generators are the pfaffians of suitable submatrices of an alternating matrix. From the graded version of the previous result, we characterize the graded Betti numbers of all 3-codimensional almost complete intersection schemes of P^r.

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