Dmodules on Smooth Toric Varieties
Abstract
Let X be a smooth toric variety. David Cox introduced the homogeneous coordinate ring S of X and its irrelevant ideal B. Extending wellknown results on projective space, Cox established the following: (1) the category of quasicoherent sheaves on X is equivalent to the category of graded Smodules modulo Btorsion, (2) the variety X is a geometric quotient of Spec(S) V(B) by a suitable torus action. We provide the Dmodule version of these results. More specifically, let A denote the ring of differential operators on Spec(S). We show that the category of Dmodules on X is equivalent to a subcategory of graded Amodules modulo Btorsion. Additionally, we prove that the characteristic variety of a Dmodule is a geometric quotient of an open subset of the characteristic variety of the associated Amodule and that holonomic Dmodules correspond to holonomic Amodules.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2000
 arXiv:
 arXiv:math/0007099
 Bibcode:
 2000math......7099M
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Rings and Algebras;
 14M25;
 16S32
 EPrint:
 AMSLaTeX, 28 pages