On Gorenstein ℚ_p-rational threefold and fourfold singularities

2025/06/18 by Jefferson Baudin, Zsolt Patakfalvi, Baudin, Jefferson +5
Mathematics · #14B05 #14F30 Secondary: 14J30 #14J35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary: 14G17

paper · pdf · doi:10.48550/arxiv.2506.15491

openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We prove that for n ≤ 4 and p > 5, quasi--Gorenstein F--pure and ℚ_p--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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Related

• An optimal gap of minimal log discrepancies of threefold non-canonical singularities
• On the canonical degrees of Gorenstein threefolds of general type
• Rationality of Fano threefolds with terminal Gorenstein singularities,\n II
• Rational and Semi-Rational Singularities
• Singularities with respect to Mather-Jacobian discrepancies