Non-Commutative Resolutions of Toric Varieties
Abstract
Let $R$ be the coordinate ring of an affine toric variety. We show that the endomorphism ring $End_R(\mathbb A),$ where $\mathbb A$ is the (finite) direct sum of all (isomorphism classes of) conic $R$-modules, has finite global dimension. Furthermore, we show that $End_R(\mathbb A)$ is a non-commutative crepant resolution if and only if the toric variety is simplicial. For toric varieties over a perfect field $k$ of prime characteristic, we show that the ring of differential operators $D_\mathsf{k}(R)$ has finite global dimension.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2018
- DOI:
- 10.48550/arXiv.1805.00492
- arXiv:
- arXiv:1805.00492
- Bibcode:
- 2018arXiv180500492F
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- Mathematics - Rings and Algebras;
- 13C14;
- 13A35;
- 16E10;
- 16S32
- E-Print:
- V2: edits, final version to appear in Advances