NonCommutative 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 noncommutative 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 eprints
 Pub Date:
 May 2018
 arXiv:
 arXiv:1805.00492
 Bibcode:
 2018arXiv180500492F
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 Mathematics  Rings and Algebras;
 13C14;
 13A35;
 16E10;
 16S32
 EPrint:
 V2: edits, final version to appear in Advances