D-modules 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 well-known results on projective space, Cox established the following: (1) the category of quasi-coherent sheaves on X is equivalent to the category of graded S-modules modulo B-torsion, (2) the variety X is a geometric quotient of Spec(S) V(B) by a suitable torus action. We provide the D-module version of these results. More specifically, let A denote the ring of differential operators on Spec(S). We show that the category of D-modules on X is equivalent to a subcategory of graded A-modules modulo B-torsion. Additionally, we prove that the characteristic variety of a D-module is a geometric quotient of an open subset of the characteristic variety of the associated A-module and that holonomic D-modules correspond to holonomic A-modules.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- July 2000
- DOI:
- 10.48550/arXiv.math/0007099
- arXiv:
- arXiv:math/0007099
- Bibcode:
- 2000math......7099M
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Rings and Algebras;
- 14M25;
- 16S32
- E-Print:
- AMS-LaTeX, 28 pages