2010/05/03 by Luchezar L. Avramov, Luchézar L. Avramov, Avramov, Luchezar L. +5
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC
paper · pdf · doi:10.48550/arxiv.1005.0325
To appear in the special issue of the Journal of Commutative Algebra, dedicated to Ralf Froeberg's 65th birthday.
arxiv created 2010/05/03 · openalex publication_date 2010/05/03 · arxiv updated 2010/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is concerned with graded modules M with linear resolutions over a standard graded algebra R. It is proved that if such an M has Hilbert series HM(s) of the form psd+qsd+1, then the algebra R is Koszul; if, in addition, M has constant Betti numbers, then HR(s)=1+es+(e-1)s2. When HR(s)=1+es+rs2 with r≤ e-1, and R is Gorenstein or e=r+1≤ 3, it is proved that generic R-modules with q≤(e-1)p are linear.