Statements (35)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
|
| gptkbp:anticanonicalMap |
gives embedding for degree ≥ 3
|
| gptkbp:automorphismGroup |
finite for general Del Pezzo surface
|
| gptkbp:class |
by degree (1 to 9)
|
| gptkbp:definedIn |
smooth projective algebraic surface with ample anticanonical divisor
|
| gptkbp:degree |
2
1 3 4 5 6 7 8 |
| gptkbp:degree1 |
blow-up of projective plane at 8 points in general position
|
| gptkbp:degree2 |
double cover of projective plane branched over quartic curve
|
| gptkbp:degree3 |
cubic surface in projective 3-space
|
| gptkbp:degree8 |
quadric surface or blow-up of projective plane at one point
|
| gptkbp:degree9 |
projective plane
|
| gptkbp:example |
projective plane blown up at up to 8 points
quadric surface |
| gptkbp:field |
algebraically closed field
|
| https://www.w3.org/2000/01/rdf-schema#label |
Del Pezzo surfaces
|
| gptkbp:line |
16 lines on degree 4 Del Pezzo surface
27 lines on cubic surface (degree 3) |
| gptkbp:namedAfter |
gptkb:Pasquale_del_Pezzo
|
| gptkbp:PicardNumber |
1 for generic Del Pezzo surface
|
| gptkbp:relatedTo |
gptkb:Fano_varieties
gptkb:Enriques_surfaces gptkb:K3_surfaces Cubic surfaces Rational surfaces |
| gptkbp:studiedIn |
gptkb:algebraic_geometry
|
| gptkbp:usedIn |
classification of algebraic surfaces
|
| gptkbp:bfsParent |
gptkb:Fano_varieties
|
| gptkbp:bfsLayer |
6
|