Short Koszul modules

Details Short Koszul modules Short Koszul modules

2010-05-03

arxiv.org/abs/1005.0325v1

Mathematics

Commutative Algebra

To appear in the special issue of the Journal of Commutative Algebra, dedicated to Ralf Froeberg's 65th birthday.

Scientific paper

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 $H_M(s)$ of the form $ps^d+qs^{d+1}$, then the algebra R is Koszul; if, in addition, M has constant Betti numbers, then $H_R(s)=1+es+(e-1)s^{2}$. When $H_R(s)=1+es+rs^{2}$ with $r\leq e-1$, and R is Gorenstein or $e=r+1\le 3$, it is proved that generic R-modules with $q\leq(e-1)p$ are linear.

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