Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
linear systems
projective varieties |
| gptkbp:field |
gptkb:algebraic_geometry
|
| gptkbp:generalizes |
generic smoothness theorem
|
| gptkbp:hasVariant |
gptkb:Bertini's_irreducibility_theorem
Bertini's theorem on irreducibility |
| https://www.w3.org/2000/01/rdf-schema#label |
Bertini's theorem
|
| gptkbp:namedAfter |
gptkb:Eugenio_Bertini
|
| gptkbp:publishedIn |
gptkb:Annali_di_Matematica_Pura_ed_Applicata
|
| gptkbp:relatedTo |
base locus
generic smoothness hyperplane section |
| 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:yearProposed |
1882
|
| gptkbp:bfsParent |
gptkb:Poonen's_Bertini_theorem
|
| gptkbp:bfsLayer |
6
|