MMP (Minimal Model Program)

URI: https://gptkb.org/entity/MMP_(Minimal_Model_Program)

GPTKB entity

Statements (54)

Predicate	Object
gptkbp:instanceOf	gptkb:logic
gptkbp:alsoKnownAs	gptkb:Minimal_Model_Program
gptkbp:application	gptkb:string_theory moduli theory classification of higher-dimensional varieties
gptkbp:developedBy	1980s
gptkbp:field	gptkb:algebraic_geometry
gptkbp:goal	classify algebraic varieties construct minimal models study birational geometry
https://www.w3.org/2000/01/rdf-schema#label	MMP (Minimal Model Program)
gptkbp:influencedBy	gptkb:Italian_school_of_algebraic_geometry gptkb:Enriques–Kodaira_classification
gptkbp:notableAchievement	classification of algebraic surfaces Mori's proof of the existence of minimal models for 3-folds existence of flips in dimension 3 termination of flips in dimension 3
gptkbp:notablePerson	gptkb:Shigefumi_Mori gptkb:János_Kollár gptkb:V._V._Shokurov gptkb:Vyacheslav_Shokurov gptkb:Yujiro_Kawamata gptkb:Miles_Reid
gptkbp:openProblem	existence of minimal models in all dimensions termination of flips in higher dimensions
gptkbp:originatedIn	gptkb:Shigefumi_Mori
gptkbp:relatedConcept	gptkb:Fano_variety gptkb:Mori_theory birational geometry minimal model flip flop canonical model divisorial contraction
gptkbp:relatedTo	gptkb:Kodaira_dimension gptkb:Kawamata_log_terminal_singularities gptkb:log_minimal_model_program gptkb:Mori_dream_space gptkb:Sarkisov_program gptkb:abundance_conjecture gptkb:canonical_singularities gptkb:log_canonical_singularities extremal ray ample divisor canonical bundle formula cone theorem contraction theorem nef divisor rational connectedness rational singularities singularities of pairs terminal singularities
gptkbp:bfsParent	gptkb:Resolution_of_singularities
gptkbp:bfsLayer	6