2005/03/31 by K. De Naeghel, M. Van den Bergh
Mathematics · #math.RA #math.AG #msc:16D25 #msc:16S38 #msc:18E30
published as Journal of Algebra 283 (2005) 399-429 · 25 pages with 16 figures
arxiv created 2005/03/31 · arxiv updated 2009/12/01
We determine the possible Hilbert functions of graded rank one torsion free modules over three dimensional Artin-Schelter regular algebras. It turns out that, as in the commutative case, they are related to Castelnuovo functions. From this we obtain an intrinsic proof that the space of torsion free rank one modules on a non-commutative projective plane is connected. A different proof of this fact, based on deformation theoretic methods and the known commutative case has recently been given by Nevins and Stafford. For the Weyl algebra it was proved by Wilson.