Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493466 | Journal of Algebra | 2005 | 31 Pages |
Abstract
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 P2 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 [Sklyanin algebras and Hilbert schemes of points, math.AG/0310045]. For the Weyl algebra it was proved by Wilson [Invent. Math. 133 (1) (1998) 1-41].
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Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Koen De Naeghel, Michel Van den Bergh,