Short Koszul modules
Avramov, Luchezar L. · Iyengar, Srikanth B. · Sega, Liana M.
Original · EN
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.
English translation
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