Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Resolution of singularities

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0, this was proved by Heisuke Hironaka in 1964; while for varieties of dimension at least 4 over fields of characteristic…

Characters, Resolution of singularities of curves & Resolution of singularities of surfaces

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Resolution of singularities. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Resolution of singularities of curves

Algebraic curveMuhly & Zariski (1939)NewtonPuiseux seriesRiemann
15 related topics

Resolution of singularities of surfaces

ExcellentLocal uniformization theoremFinite setLocal uniformizationIf and only if
8 related topics

Method of proof in characteristic zero

Ideal sheafExceptional divisorsHilbert–Samuel function
3 related topics

Examples

Whitney umbrellaPinch pointAtiyah flopSmall resolutionsToric varieties
5 related topics

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Definitions

Resolution of singularities of curves

Resolution of singularities of surfaces

Zariski's method

Resolution for schemes and status of the problem

Method of proof in characteristic zero

Examples

Bibliography

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Resolution of singularities

Nodes82
Edges81
Triples279
Avg. degree1.98
Density0.02439
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Resolution of singularities

Top relations

related to Bibliography · 199
Resolution of singularities → Abhyankar, Abramovich, Acad, Acta Math, Adolfo, Advances, Alberto Tognoli, Algebra, Algebraic, Algebraic Curve, Algebraic Geometry, Algebraic Surface, Amer, American Math, American Mathematical Soc, American Mathematical Society, Angewandte Mathematik, Ann, Annals, Arcata
related to External links · 17
Resolution of singularities → Archived, AustriaLecture, Hironaka, Italy, June, Notes, Obergurgl, Resolution, September, Singularities, Singularities Tirol, Some, Summer School, Tirol, Trieste, Wayback Machine, Working Week
related to Resolution of singularities of surfaces · 15
Resolution of singularities → Abhyankar, Albanese, Chisini, Del Pezzo, However, In, Levi, Lipman, Resolution, Severi, Surfaces, The, There, Walker, Zariski
related to Hironaka's method · 14
Resolution of singularities → Bierstone, Encinas, For, Hauser, He, Hironaka, Hironaka's, Kollár, Milman, Resolution, Simplified, Some, Villamayor, Wlodarczyk
related to De Jong's method · 8
Resolution of singularities → Abramovich, Bogomolov, De Jong, De Jong's, Jong, Jung's, Pantev, This
related to Abhyankar's method · 7
Resolution of singularities → Abhyankar, Abhyankar's, Albanese's, CossartandPiltant, Cutkosky, The, Zariski's
related to Zariski's method · 7
Resolution of singularities → Although, For, He, Riemann, The, Zariski, Zariski's
related to Definitions · 5
Resolution of singularities → In, More, Originally, Suppose, The
related to Newton's method · 3
Resolution of singularities → Newton, Puiseux, Resolution
related to Resolution of singularities of curves · 3
Resolution of singularities → Every, In, Kollár

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

singularities resolution doi singular characteristic points variety 10 method blowing math mr singularity one algebraic smooth dimension surfaces proof resolve

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Resolution of singularitiesrelated to Abhyankar's methodAbhyankar0.60section
Resolution of singularitiesrelated to Abhyankar's methodThe0.60section
Resolution of singularitiesrelated to Abhyankar's methodZariski's0.60section
Resolution of singularitiesrelated to Abhyankar's methodAlbanese's0.60section
Resolution of singularitiesrelated to Abhyankar's methodCutkosky0.60section
Resolution of singularitiesrelated to Abhyankar's methodAbhyankar's0.60section
Resolution of singularitiesrelated to Abhyankar's methodCossartandPiltant0.60section
Resolution of singularitiesrelated to BibliographyLock-green0.60section
Resolution of singularitiesrelated to BibliographyLock-gray-alt-20.60section
Resolution of singularitiesrelated to BibliographyLock-red-alt-20.60section
Resolution of singularitiesrelated to BibliographyWikisource-logo0.60section
Resolution of singularitiesrelated to BibliographyAbhyankar0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.