Purely log terminal threefolds with non-normal centres in characteristic two

2016/07/28 by Paolo Cascini, Hiromu Tanaka, Cascini, Paolo +1 · 3 citations
Mathematics · #14E30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1607.08590

openalex publication_date 2016/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We show that many classical results of the minimal model programme do not hold over an algebraically closed field of characteristic two. Indeed, we construct a three dimensional plt pair whose codimension one part is not normal, a three dimensional klt singularity which is not rational nor Cohen-Macaulay, and a klt Fano threefold with non-trivial intermediate cohomology.

Cited by

• Non-extendable MMPs
• On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type
• On Gorenstein ℚ_p-rational threefold and fourfold singularities

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