The Hironaka theorem on resolution of singularities (Or: A proof we always wanted to understand)
From MaRDI portal
Publication:4708794
DOI10.1090/S0273-0979-03-00982-0zbMath1030.14007WikidataQ57601957 ScholiaQ57601957MaRDI QIDQ4708794
Publication date: 19 June 2003
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Modifications; resolution of singularities (complex-analytic aspects) (32S45) Local complex singularities (32S05) Invariants of analytic local rings (32S10)
Related Items
Good formal structures for flat meromorphic connections. III: Irregularity and turning loci, Lifting for Simplicity: Concise Descriptions of Convex Sets, Hypersurface singularities in positive characteristic, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup></mml:math>-theory for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>∂</mml:mi> <mml:mo>¯</mml:mo></mml:mover></mml:math>-operator on complex spaces with isolated singularities, The Dolbeault complex with weights according to normal crossings, The \({\overline{\partial}}\)-equation on homogeneous varieties with an isolated singularity, Formal desingularization of surfaces: The Jung method revisited, Simple Hironaka resolution in characteristic zero, Log canonical models for the moduli space of curves: The first divisorial contraction, A simpler proof of toroidalization of morphisms from 3-folds to surfaces, Singularities of rational inner functions in higher dimensions, Telescopic actions, Sublevel-set estimates over global domains, A procedure for computing the log canonical threshold of a binomial ideal, Perron transforms and Hironaka's game, Degenerating Hermitian metrics and spectral geometry of the canonical bundle, Scales, blow-up and quasimode constructions, On constructive desingularization, Elimination with applications to singularities in positive characteristic, Hypersurfaces and their singularities in partial correlation testing, \(L^2\)-theory for the \(\overline{\partial}\)-operator on compact complex spaces, Partial local resolution by characteristic zero methods, A \(\overline{\partial}\)-theoretical proof of Hartogs' extension theorem on Stein spaces with isolated singularities, Toward resolution of singularities over a field of positive characteristic. I. Foundation; the language of the idealistic filtration, Equimultiplicity, algebraic elimination, and blowing-up, Today’s menu: Geometry and resolution of singular algebraic surfaces, Blowups in tame monomial ideals, Lie symmetries and CR geometry, Compactness of the \(\bar{\partial}\)-Neumann operator on singular complex spaces, The winning strategy for Hironaka's polyhedra game is almost arbitrary, Singularities in positive characteristic, stratification and simplification of the singular locus, Resolution of singularities for multi-loop integrals, Characterizing the increase of the residual order under blowup in positive characteristic, Noncommutative resolutions of discriminants, \(L^2\)-properties of the \(\overline{\partial}\) and the \(\overline{\partial}\)-Neumann operator on spaces with isolated singularities, Resolution of singularities and geometric proofs of the Łojasiewicz inequalities, On the simplication of singularities by blowing up at equimultiple centers, ABOUT THE $\bar{\partial}$-EQUATION AT ISOLATED SINGULARITIES WITH REGULAR EXCEPTIONAL SET, Łojasiewicz exponents and resolution of singularities, On the Laplace–Beltrami operator on compact complex spaces, A fast flatness testing criterion in characteristic zero, On the problem of resolution of singularities in positive characteristic (Or: A proof we are still waiting for), A simplified proof of desingularization and applications, Computation of blowing up centers
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Two computational techniques for singularity resolution
- Semianalytic and subanalytic sets
- Good points and constructive resolution of singularities
- Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
- Automated resolution of singularities for hypersurfaces
- Strong resolution of singularities in characteristic zero
- Computation of blowing up centers
- A new proof of desingularization over fields of characteristic zero
- A simplified proof of desingularization and applications
- Resolution of singularities of an algebraic variety over a field of characteristic zero. I
- Constructiveness of Hironaka's resolution
- A STRENGTHENING OF RESOLUTION OF SINGULARITIES IN CHARACTERISTIC ZERO
- Uniformization of Analytic Spaces
- Resolution of Singularities
- Patching local uniformizations
- Automated Deduction in Geometry
- Strengthening the theorem of embedded desingularization
