Strong resolution of singularities in characteristic zero

2002/12/31 by S. Encinas, H. Hauser · 5 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Polynomial and algebraic computation #Resolution of singularities #Mathematics #Zero (linguistics) #Resolution (logic) #Gravitational singularity #Pure mathematics #Field (mathematics) #Mathematical analysis #Computer science #Artificial intelligence

paper · pdf · doi:10.1007/pl00012443

openalex publication_date 2002/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

We present a concise proof for the existence and construction of a strong resolution of excellent schemes of finite type over a field of characteristic zero. Our proof is based on earlier work of Villamayor, Encinas-Villamayor and Bierstone-Milman. It proposes some substantial simplifications which may be helpful for a better understanding of how to prove Hironaka's famous theorem on embedded resolution of singularities.

Citations

• Smoothness, Semistability, and Toroidal Geometry
• 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

Cited by

• Simple Hironaka resolution in characteristic zero
• The Hironaka theorem on resolution of singularities (Or: A proof we always wanted to understand)
• 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 [wikipedia]