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In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its origins in the classical birational geometry of surfaces studied by the Italian school, and is currently an active research area within algebraic geometry.

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rdfs:label	Minimal model program (en)
rdfs:comment	In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its origins in the classical birational geometry of surfaces studied by the Italian school, and is currently an active research area within algebraic geometry. (en)
sameAs	Minimal model program
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Main dbt:Reflist dbt:Eom
Subject	3-folds Algebraic geometry Birational geometry
gold:hypernym	Part
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Minimal_model_program?oldid=1018353870&ns=0
Wikipage page ID	15148924 (xsd:integer)
page length (characters) of wiki page	9692 (xsd:nonNegativeInteger)
Wikipage revision ID	1018353870 (xsd:integer)
Link from a Wikipage to another Wikipage	Flip (mathematics) Projective variety Smooth scheme Abundance conjecture Algebraic geometry Algebraic variety Ample line bundle Birational geometry Vyacheslav Shokurov Bulletin of the AMS Cambridge University Press Canonical bundle Canonical singularity Castelnuovo's contraction theorem 3-folds Algebraic geometry Birational geometry Caucher Birkar James McKernan Journal of the American Mathematical Society Divisor (algebraic geometry) Christopher Hacon Shigefumi Mori Springer Science+Business Media Cone of curves Contraction morphism Morphism of algebraic varieties Fano fibration Guido Castelnuovo Isomorphism Italian school of algebraic geometry Kodaira dimension Nef line bundle Rational surface
has abstract	In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its origins in the classical birational geometry of surfaces studied by the Italian school, and is currently an active research area within algebraic geometry. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Minimal_model_program
is Wikipage redirect of	Classification of algebraic varieties Minimal model (birational geometry) Minimal model conjecture Mori's minimal model program Mori program Mori theory
is Link from a Wikipage to another Wikipage of	Flip (mathematics) Flix (programming language) Noether inequality Néron model 3-fold Abundance conjecture Birational geometry Mori dream space Breakthrough Prize in Mathematics Canonical bundle Canonical ring Canonical singularity Castelnuovo's contraction theorem Caucher Birkar Glossary of algebraic geometry Michael Atiyah Chenyang Xu János Kollár K-stability of Fano varieties Cohen–Macaulay ring Coherent sheaf cohomology Complex geometry Cone of curves Contraction morphism List of University of Utah people List of algebraic geometry topics List of complex and algebraic surfaces Minimal model Enriques–Kodaira classification Iitaka dimension Fano fibration Fano variety Field (mathematics) Fields Medal Intersection theory Kähler–Einstein metric Classification of algebraic varieties Kodaira dimension MMP Minimal model (birational geometry) Minimal model conjecture Mori's minimal model program

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