Noncommutative resolution of toric singularities: An application of Frobenius morphism of noncommutative blowup

Abstract

Using Frobenius morphisms of noncommutative blowups, we prove that every normal toric singularity has a standard noncommutative resolution.

This paper has been withdrawn by the author due to a crucial error, which was pointed out by a referee. The error lies in the assertion in page 8 that ${\mathfrak{C}}_G$ is a translation of the cone $\mathfrak{C}$. It is not a cone in general. Accordingly an assertion about the preservation of projective modules over a noncommutative ring associated to a toric singularity is no longer valid

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• Non-commutative resolutions of quotient singularities