Resolution of Singularities for 3-folds in positive characteristic

2006/06/21 by Steven Dale Cutkosky, Cutkosky, Steven Dale · 1 citation
Mathematics · #14J17 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #math.AC #math.AG #msc:14J17

paper · pdf · doi:10.48550/arxiv.math/0606530

55 pages. In this final version, which is to appear in the American Journal of Mathematics, complete details of the proof of embedded resolution of surfaces have been added in. Two sections have been added after the introduction, giving an outline of the proof, and discussing related results and extensions of the material proved in this paper

openalex publication_date 2006/06/21 · arxiv created 2007/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper a concise, complete proof of resolution of singularities of 3-folds in positive characteristic (>5) is given. The first proof of this theorem was given by Abhyankar in 1966. The resolution morphism in our proof is an isomorphism over the nonsingular locus.

Citations

• Resolution of Singularities -- Seattle Lecture
• Smoothness, Semistability, and Toroidal Geometry
• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Cited by

• The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings

Related

• Resolution of 1-foliations singularities on surfaces and threefolds
• Minimal resolutions of threefolds
• Toward resolution of singularities over a field of positive characteristic Part I. Foundation of the program: the language of the idealistic filtration
• Resolution of singularities of an idealistic filtration in dimension 3 after Benito-Villamayor
• Some natural properties of constructive resolution of singularities