Analysis shows that quasi-Gorenstein singularities are canonical in threefolds and fourfolds, suggesting important relationships in algebraic geometry.
We prove that for n ≤ 4 and $p > 5$, quasi--Gorenstein F--pure and Qₚ--rational n--fold singularities are canonical. This is analogous to the usual fact that rational Gorenstein singularities are canonical. The proof is based on a careful analysis of the dual complex of a dlt modification of a log canonical singularity. The result for $n = 4$ is contingent upon the existence of log resolutions.
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Baudin et al. (2025) studied this question.
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