Resolution of singularities

URI: https://gptkb.org/entity/Resolution_of_singularities
GPTKB entity
Statements (66)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo algebraic varieties
schemes
gptkbp:describes process of modifying a singular algebraic variety to obtain a non-singular variety
gptkbp:field gptkb:algebraic_geometry
https://www.w3.org/2000/01/rdf-schema#label Resolution of singularities
gptkbp:introduced gptkb:Oscar_Zariski
gptkbp:notable_for gptkb:Hironaka's_theorem
gptkbp:notablePerson gptkb:Jean-Pierre_Serre
gptkb:Jean_Giraud
gptkb:Shreeram_Abhyankar
gptkb:David_Mumford
gptkb:Pierre_Deligne
gptkb:Edward_Bierstone
gptkb:Herwig_Hauser
gptkb:Hiroshi_Matsumura
gptkb:Joseph_Lipman
gptkb:Mark_Spivakovsky
gptkb:Steven_Dale_Cutkosky
gptkb:Vladimir_Abramovich_Iskovskikh
gptkbp:notablePublication gptkb:Annals_of_Mathematics,_1964,_Hironaka's_paper
gptkbp:openProblem resolution in positive characteristic
gptkbp:provenBy gptkb:Heisuke_Hironaka
gptkbp:relatedConcept blowup
desingularization
singular point
smooth variety
gptkbp:relatedTo gptkb:ADE_classification
gptkb:Du_Val_singularity
gptkb:MMP_(Minimal_Model_Program)
gptkb:Macaulayfication
gptkb:Nash_blowing-up
gptkb:Zariski's_lemma
gptkb:Zariski's_main_theorem
gptkb:Zariski's_patching
gptkb:Zariski's_purity_theorem
gptkb:minimal_model_program
gptkb:toric_varieties
gptkb:weak_factorization_theorem
algorithmic resolution
alterations (in positive characteristic)
canonical resolution
canonical singularity
desingularization algorithm
embedded resolution
functorial resolution
local uniformization
log canonical singularity
log resolution
modification (algebraic geometry)
rational singularity
resolution of curve singularities
resolution of surface singularities
resolution of threefold singularities
simple normal crossings
simple singularity
terminal singularity
gptkbp:result every algebraic variety over a field of characteristic zero admits a resolution of singularities
gptkbp:usedIn gptkb:string_theory
number theory
birational geometry
complex geometry
moduli theory
gptkbp:yearProved 1964
gptkbp:bfsParent gptkb:algebraic_geometry
gptkbp:bfsLayer 5