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gptkbp:instanceOf
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gptkb:geometry
gptkb:mathematical_concept
Complex manifold
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gptkbp:automorphismGroup
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gptkb:PGL(3,C)
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gptkbp:Betti_number_b2
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1
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gptkbp:can_be_blown_up
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at points
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gptkbp:contains
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complex algebraic curves
complex projective lines
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gptkbp:definedIn
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gptkb:Complex_numbers
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gptkbp:dimensions
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2 (complex)
4 (real)
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gptkbp:Euler_characteristic
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3
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gptkbp:first_Chern_class
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3
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gptkbp:fundamentalGroup
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trivial
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gptkbp:heldBy
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gptkb:algebraic_geometry
gptkb:Fano_variety
gptkb:Del_Pezzo_surface
gptkb:projective_algebraic_variety
surface
Hausdorff space
Kähler manifold
compact space
connected space
homogeneous space
smooth variety
symmetric space
rational surface
simply connected space
example in Hodge theory
example in intersection theory
example in sheaf cohomology
example of compact complex surface
example of nontrivial topology
generalization of real projective plane
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gptkbp:Hodge_diamond
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1 0 0 1 0 1
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gptkbp:homogeneous_coordinates
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[z0:z1:z2]
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https://www.w3.org/2000/01/rdf-schema#label
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Complex projective plane
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gptkbp:intersection_form
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1
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gptkbp:notation
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gptkb:CP^2
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gptkbp:Picard_group
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Z
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gptkbp:relatedTo
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gptkb:geometry
gptkb:Veronese_embedding
gptkb:twistor_space
Grassmannian
flag variety
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gptkbp:used_in
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gptkb:algebraic_geometry
gptkb:topology
complex geometry
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gptkbp:bfsParent
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gptkb:Projective_plane
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gptkbp:bfsLayer
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7
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