Resolution of singularities for 3-folds in positive characteristic

2009/02/01 by Steven Dale Cutkosky · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Homotopy and Cohomology in Algebraic Topology #Mathematics #Gravitational singularity #Resolution of singularities #Resolution (logic) #Geometry #Artificial intelligence #Mathematical analysis #Computer science

paper · doi:10.1353/ajm.0.0036

openalex publication_date 2009/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

A concise, complete proof of resolution of singularities of 3-folds in positive characteristic >5 is given. Abhyankar first proved this theorem in 1966.

Citations

• Smoothness, Semistability, and Toroidal Geometry
• Toward resolution of singularities over a field of positive characteristic Part I. Foundation of the program: the language of the idealistic filtration
• Simple Hironaka resolution in characteristic zero
• The Hironaka theorem on resolution of singularities (Or: A proof we always wanted to understand)
• Resolution of singularities of threefolds in positive characteristic II
• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• Trasformazione birazionale di una superficie algebrica qualunque in un’altra priva di punti multipli
• Strong resolution of singularities in characteristic zero
• Reduction of the Singularities of Algebraic Three Dimensional Varieties

Cited by

• Resolution of singularities [wikipedia]