Ideal classes of three dimensional Artin-Schelter regular algebras

Details Ideal classes of three dimensional Artin-Schelter regular algebras Ideal classes of three dimensional Artin-Schelter regular algebras

2005-03-31

arxiv.org/abs/math/0503730v1

Journal of Algebra 283 (2005) 399-429

Mathematics

Rings and Algebras

25 pages with 16 figures

Scientific paper

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.

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