Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero

URI: https://gptkb.org/entity/Resolution_of_Singularities_of_an_Algebraic_Variety_Over_a_Field_of_Characteristic_Zero
GPTKB entity
Statements (22)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo algebraic varieties
fields of characteristic zero
gptkbp:contributedTo gptkb:Heisuke_Hironaka
gptkbp:field gptkb:algebraic_geometry
https://www.w3.org/2000/01/rdf-schema#label Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero
gptkbp:influenced birational geometry
modern algebraic geometry
moduli theory
gptkbp:method blowing up along smooth centers
inductive process
gptkbp:publishedIn Annals of Mathematics, 1964
gptkbp:relatedConcept gptkb:blowup_(algebraic_geometry)
singularities
desingularization
smooth variety
gptkbp:resultedIn Fields Medal for Heisuke Hironaka
gptkbp:sentence Every algebraic variety over a field of characteristic zero admits a resolution of singularities.
gptkbp:status open in positive characteristic
gptkbp:yearProved 1964
gptkbp:bfsParent gptkb:Annals_of_Mathematics,_1964,_Hironaka's_paper
gptkbp:bfsLayer 7