Normality of minimal log canonical centers of threefolds in mixed and positive characteristic

TL;DR

This paper proves the normality of minimal log canonical centers on threefold pairs over perfect residue fields with characteristic not equal to 2, 3, or 5, and discusses seminormality of unions of such centers.

Contribution

It establishes normality results for minimal log canonical centers in mixed and positive characteristic, and explores seminormality conditions with explicit examples.

Findings

Normality of minimal log canonical centers in specified characteristics

Seminormality of unions of log canonical centers under certain conditions

Counterexample of non-seminormal center in characteristic 3

Abstract

We prove the normality of minimal log canonical centers on threefold pairs which residue fields are perfect of residue characteristics $p\neq 2,3 $ and $5$. We also show that the union of all log canonical centers on threefold pairs with standard coefficients are seminormal provided that the residue characteristic is large enough. We provide an example of a non-seminormal log canonical center on a threefold in characteristic $3$, and give sufficient conditions to construct similar examples.