On the F-purity of isolated log canonical singularities

Abstract

A singularity in characteristic zero is said to be of dense F-pure type if its modulo p reduction is locally F-split for infinitely many p. We prove that if $x\in X$ is an isolated log canonical singularity with $\mu (x\in X)\le 2$ (see Definition 1.4 for the definition of the invariant $\mu$), then it is of dense F-pure type. As a corollary, we prove the equivalence of log canonicity and being of dense F-pure type in the case of three-dimensional isolated singularities.

16 pages, v2: Corollary 3.7 reformulated, other minor changes

References in corpus (2)

• Introduction to the log minimal model program for log canonical pairs
• F-purity versus log canonicity for polynomials

Cited by in corpus (3)

• Characterization of varieties of Fano type via singularities of Cox rings
• Mori dream spaces of Calabi-Yau type and the log canonicity of the Cox rings
• Surfaces of globally $F$-regular and $F$-split type