Ideals with Larger Projective Dimension and Regularity

2011/01/18 by Jesse S. Beder, Beder, Jesse, Jason McCullough +9 · 1 citation
Mathematics · #13D05 #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.1101.3368

openalex publication_date 2011/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given in [Cav04] and [McC]. In particular, we describe a family of three-generated homogeneous ideals in arbitrary characteristic whose projective dimension grows asymptotically as sqrtd^(sqrt(d) - 1).

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