Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
|
| gptkbp:anticanonicalBundle |
ample
|
| gptkbp:anticanonicalMap |
2-to-1 for degree 2
birational for degree ≥ 3 degree 1 for degree 1 |
| gptkbp:automorphismGroup |
finite for degree ≤ 5
|
| gptkbp:class |
classified by degree
|
| gptkbp:defines |
A smooth projective algebraic surface with ample anticanonical bundle
|
| gptkbp:degree |
integer between 1 and 9
|
| gptkbp:degree1 |
blow-up of projective plane at 8 points
|
| gptkbp:degree2 |
double cover of projective plane branched over quartic curve
|
| gptkbp:degree3 |
cubic surface in projective 3-space
|
| gptkbp:degree4 |
intersection of two quadrics in projective 4-space
|
| gptkbp:degree5 |
blow-up of projective plane at 4 points
|
| gptkbp:degree6 |
blow-up of projective plane at 3 points
|
| gptkbp:degree7 |
blow-up of projective plane at 2 points
|
| gptkbp:degree8 |
blow-up of projective plane at 1 point
|
| gptkbp:degree9 |
projective plane
|
| gptkbp:dimensions |
2
|
| gptkbp:example |
product of two projective lines (degree 8)
projective plane blown up at up to 8 points in general position |
| gptkbp:field |
gptkb:algebraic_geometry
algebraically closed field |
| https://www.w3.org/2000/01/rdf-schema#label |
Del Pezzo surface
|
| gptkbp:importantFor |
classification of algebraic surfaces
|
| gptkbp:linesOnDegree3 |
27
|
| gptkbp:linesOnDegree4 |
16
|
| gptkbp:linesOnDegree5 |
10
|
| gptkbp:linesOnDegree6 |
6
|
| gptkbp:linesOnDegree7 |
3
|
| gptkbp:linesOnDegree8 |
1
|
| gptkbp:linesOnDegree9 |
0
|
| gptkbp:linesOnSurface |
finite number depending on degree
|
| gptkbp:namedAfter |
gptkb:Pasquale_del_Pezzo
|
| gptkbp:PicardNumber |
1 for generic Del Pezzo surface
|
| gptkbp:relatedTo |
gptkb:Weyl_group
gptkb:Fano_variety gptkb:K3_surface gptkb:Mori_theory gptkb:Enriques_surface gptkb:Galois_cohomology gptkb:Exceptional_Lie_algebras gptkb:Rational_surface gptkb:Cubic_surface gptkb:Root_system Birational geometry Minimal model program |
| gptkbp:singularDelPezzoSurface |
possible if points are not in general position
|
| gptkbp:studiedBy |
gptkb:Pasquale_del_Pezzo
|
| gptkbp:bfsParent |
gptkb:Cubic_surface
|
| gptkbp:bfsLayer |
6
|