Non-quasi-$F$-split canonical affine fourfolds exist in every characteristic

TL;DR

This paper constructs specific four-dimensional algebraic varieties in positive characteristic that are canonical, Gorenstein, and affine, and importantly, are not quasi-$F$-split, expanding understanding of their properties.

Contribution

It provides the first explicit examples of canonical affine fourfolds in every positive characteristic that are not quasi-$F$-split.

Findings

Existence of non-quasi-$F$-split canonical affine fourfolds in all positive characteristics

Construction method applicable in every positive characteristic

Advances understanding of $F$-singularities in algebraic geometry

Abstract

We construct canonical $\mathbb{Q}$-factorial Gorenstein affine fourfolds in every positive characteristic that are not quasi-$F$-split.