Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
gptkb:mathematical_concept |
| gptkbp:anticanonical_bundle |
Ample
|
| gptkbp:class |
Classified in dimension 2 (Del Pezzo surfaces)
Partially classified in dimension 3 |
| gptkbp:defines |
A compact Kähler manifold with ample anticanonical bundle
|
| gptkbp:dimensions |
Can be any positive integer
|
| gptkbp:example |
gptkb:geometry
gptkb:Del_Pezzo_surface gptkb:Smooth_quadric_hypersurface |
| gptkbp:field |
gptkb:Algebraic_geometry
|
| gptkbp:first_Chern_class |
Positive
|
| https://www.w3.org/2000/01/rdf-schema#label |
Fano manifold
|
| gptkbp:importantFor |
Central in birational geometry
Key in minimal model program |
| gptkbp:namedAfter |
gptkb:Gino_Fano
|
| gptkbp:property |
Hodge numbers h^{p,0}=0 for p>0
Rationally connected Simply connected |
| gptkbp:rank |
gptkb:Complex_numbers
|
| gptkbp:relatedTo |
gptkb:K3_surface
gptkb:Mori_theory Kähler manifold Minimal model program |
| gptkbp:studiedBy |
Algebraic geometers
|
| gptkbp:bfsParent |
gptkb:Fano_metric
|
| gptkbp:bfsLayer |
6
|