Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
linear systems
projective varieties |
| gptkbp:field |
gptkb:algebraic_geometry
|
| gptkbp:firstPublished |
late 19th century
|
| https://www.w3.org/2000/01/rdf-schema#label |
Bertini theorem
|
| gptkbp:namedAfter |
gptkb:Eugenio_Bertini
|
| gptkbp:relatedTo |
gptkb:Bertini's_irreducibility_theorem
gptkb:Bertini's_smoothness_theorem |
| gptkbp:sentence |
A general member of a linear system on a smooth variety is smooth outside the base locus.
A general hyperplane section of a smooth projective variety is smooth. |
| gptkbp:usedIn |
intersection theory
algebraic geometry proofs |
| gptkbp:bfsParent |
gptkb:Théorèmes_de_Bertini_et_applications
|
| gptkbp:bfsLayer |
7
|