The Hironaka theorem on resolution of singularities (Or: A proof we always wanted to understand)

2003/05/06 by H. Hauser · 6 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Commutative Algebra and Its Applications #Resolution of singularities #Mathematics #Gravitational singularity #Zero (linguistics) #Algebraic variety #Pure mathematics #Resolution (logic) #Field (mathematics) #Algebraic number #Algebra over a field #Mathematical analysis #Computer science #Artificial intelligence

paper · pdf · doi:10.1090/s0273-0979-03-00982-0

openalex publication_date 2003/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07

Abstract

This paper is a handyman’s manual for learning how to resolve the singularities of algebraic varieties defined over a field of characteristic zero by sequences of blowups.

Citations

• Resolution of Singularities of Embedded Algebraic Surfaces
• Resolution of Singularities of Germs in Characteristic Positive Associated with Valuation Rings of Iterated Divisor Type
• Topics in Optimal Transportation
• The Geometry of Schemes
• Smoothness, Semistability, and Toroidal Geometry
• Desingularization algorithms I. Role of exceptional divisors
• Notes on the inductive algorithm of resolution of singularities by S. Encinas and O. Villamayor
• 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
• Equivariant resolution of singularities in characteristic 0
• Good points and constructive resolution of singluarities
• Strong resolution of singularities in characteristic zero
• The concept of a simple point of an abstract algebraic variety
• Smoothness, semi-stability and alterations
• Graduate Texts in Mathematics
• Éléments de géométrie algébrique : I. Le langage des schémas

Cited by

• Simple Hironaka resolution in characteristic zero
• On the problem of resolution of singularities in positive characteristic (Or: A proof we are still waiting for)
• Resolution of singularities for 3-folds in positive characteristic
• Resolution of singularities and geometric proofsof the Łojasiewicz inequalities
• Enumerative Algebraic Geometry of Conics
• Resolution of singularities [wikipedia]