Lefschetz hyperplane theorem
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
smooth projective varieties
|
| gptkbp:describes |
relationship between the topology of a projective variety and its hyperplane sections
|
| gptkbp:field |
gptkb:algebraic_geometry
gptkb:topology |
| gptkbp:generalizes |
gptkb:Lefschetz_hyperplane_section_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lefschetz hyperplane theorem
|
| gptkbp:namedAfter |
gptkb:Solomon_Lefschetz
|
| gptkbp:relatedTo |
gptkb:Hodge_theory
gptkb:Lefschetz_fixed-point_theorem gptkb:Lefschetz_pencil |
| gptkbp:state |
the homology groups of a smooth hyperplane section are isomorphic to those of the ambient variety up to a certain degree
|
| gptkbp:usedIn |
complex algebraic geometry
singular cohomology |
| gptkbp:yearProposed |
1924
|
| gptkbp:bfsParent |
gptkb:Solomon_Lefschetz
|
| gptkbp:bfsLayer |
5
|