Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
|
| gptkbp:appearsIn |
outcomes of the minimal model program
|
| gptkbp:defines |
A normal projective variety X with a morphism f: X → Y such that X is Q-factorial, the relative Picard number is 1, and -K_X is f-ample.
|
| gptkbp:dimensions |
at least 2
|
| gptkbp:example |
Fano fibration
projective bundle over a lower-dimensional variety |
| gptkbp:field |
gptkb:algebraic_geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
Mori fiber space
|
| gptkbp:namedAfter |
gptkb:Shigefumi_Mori
|
| gptkbp:originatedIn |
birational geometry
|
| gptkbp:property |
-K_X is relatively ample
X is Q-factorial f: X → Y is a surjective morphism with connected fibers relative Picard number is 1 |
| gptkbp:relatedConcept |
gptkb:Fano_variety
minimal model flipping contraction |
| gptkbp:relatedTo |
gptkb:minimal_model_program
|
| gptkbp:usedIn |
classification of higher-dimensional algebraic varieties
|
| gptkbp:Y |
has dimension less than X
|
| gptkbp:bfsParent |
gptkb:Minimal_Model_Program
|
| gptkbp:bfsLayer |
6
|