Statements (41)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
Kähler manifold Ricci-flat manifold |
| gptkbp:category |
compact complex manifolds
non-compact complex manifolds |
| gptkbp:dimensions |
n-dimensional
|
| gptkbp:example |
gptkb:K3_surface
gptkb:quintic_threefold |
| gptkbp:firstChernClass |
zero
|
| https://www.w3.org/2000/01/rdf-schema#label |
Calabi–Yau varieties
|
| gptkbp:namedAfter |
gptkb:Eugenio_Calabi
gptkb:Shing-Tung_Yau |
| gptkbp:property |
holonomy group SU(n)
vanishing first Chern class simply connected (in many cases) trivial canonical bundle admit Ricci-flat Kähler metric can be smooth or singular can have singularities complex dimension at least 1 generalization of K3 surfaces generalization of abelian varieties generalization of elliptic curves important in compactification of extra dimensions important in supersymmetry preservation |
| gptkbp:relatedTo |
gptkb:topological_string_theory
gptkb:Calabi_conjecture moduli space Hodge numbers Yau's proof superstring compactification |
| gptkbp:studiedBy |
string theorists
algebraic geometers |
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:theoretical_physics gptkb:string_theory gptkb:mirror_symmetry |
| gptkbp:bfsParent |
gptkb:Batyrev_mirror_construction
gptkb:Fano_varieties gptkb:Higher-Dimensional_Algebraic_Geometry |
| gptkbp:bfsLayer |
6
|