P^1 × P^1

URI: https://gptkb.org/entity/P^1_×_P^1
GPTKB entity
Statements (27)
Predicate Object
gptkbp:instanceOf gptkb:algebraic_geometry
gptkb:product_variety
gptkbp:anticanonicalBundle O(2,2)
gptkbp:automorphismGroup gptkb:PGL(2)_×_PGL(2)_⋉_Z/2Z
gptkbp:BettiNumber_b_2 2
gptkbp:canonicalBundle O(-2,-2)
gptkbp:ChowRing Z[x,y]/(x^2,y^2)
gptkbp:degree 8
gptkbp:dimensions 2
gptkbp:fibrationOver P^1
gptkbp:hasBidegreeDivisors true
gptkbp:hasRuledSurfaceStructure true
gptkbp:hasTwoFibrations true
gptkbp:HodgeNumber_h^{1,1} 2
gptkbp:intersectionForm gptkb:hyperbolic_plane
gptkbp:isDelPezzoSurface true
gptkbp:isMinimal true
gptkbp:isomorphicTo gptkb:Hirzebruch_surface_F_0
gptkbp:isProjective true
gptkbp:isRational true
gptkbp:isSmooth true
gptkbp:isToric true
gptkbp:PicardGroup Z ⊕ Z
gptkbp:rank gptkb:Field
gptkbp:bfsParent gptkb:Hirzebruch_surfaces
gptkbp:bfsLayer 6
https://www.w3.org/2000/01/rdf-schema#label P^1 × P^1