Simple Hironaka resolution in characteristic zero

2005/07/13 by Jarosław Włodarczyk · 4 citations
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Homotopy and Cohomology in Algebraic Topology #Mathematics #Simple (philosophy) #Zero (linguistics) #Pure mathematics #Resolution (logic) #A priori and a posteriori #Algebra over a field #Artificial intelligence #Epistemology

paper · pdf · doi:10.1090/s0894-0347-05-00493-5

openalex publication_date 2005/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

Building upon work of Villamayor and Bierstone-Milman we give a proof of the canonical Hironaka principalization and desingularization. The idea of “homogenized ideals" introduced in the paper gives <italic>a priori</italic> the canonicity of the algorithm and radically simplifies the proof.

Citations

• Smoothness, Semistability, and Toroidal Geometry
• Desingularization algorithms I. Role of exceptional divisors
• The Hironaka theorem on resolution of singularities (Or: A proof we always wanted to understand)
• 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
• Smoothness, semi-stability and alterations
• An Example of a Non-Kahlerian Complex-Analytic Deformation of Kahlerian Complex Structures
• Desingularization of toric and binomial varieties
• Algebraic Geometry

Cited by

• 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
• Resolution of singularities [wikipedia]