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gptkbp:instanceOf
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gptkb:mathematical_concept
Kähler manifold
projective variety
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gptkbp:automorphismGroup
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gptkb:PGL(3,C)
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gptkbp:Betti_numbers
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1, 0, 1, 0, 1
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gptkbp:canonical_bundle
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gptkb:O(-3)
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gptkbp:cohomology_ring
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Z[h]/(h^3)
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gptkbp:compact
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yes
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gptkbp:contains
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complex projective line
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gptkbp:dimensions
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2
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gptkbp:Euler_characteristic
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3
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gptkbp:field
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complex numbers
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gptkbp:first_Betti_number
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0
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gptkbp:first_Chern_class
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3
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gptkbp:fourth_Betti_number
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1
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gptkbp:fundamentalGroup
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trivial
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gptkbp:has_cell_decomposition
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one 0-cell, one 2-cell, one 4-cell
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gptkbp:has_Fubini-Study_metric
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yes
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gptkbp:hasConnection
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yes
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gptkbp:hasModel
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gptkb:projective_geometry_over_C
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gptkbp:hasSpecialCase
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projective plane
complex projective space
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gptkbp:heldBy
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gptkb:algebraic_geometry
Kähler manifold
simply connected space
compact complex surface
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gptkbp:homogeneous_space_of
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gptkb:PGL(3,C)
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gptkbp:homology_group_H_2
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Z
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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:is_a_del_Pezzo_surface
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yes
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gptkbp:is_homogeneous_space
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yes
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gptkbp:is_not_homeomorphic_to
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gptkb:quaternionic_projective_plane
gptkb:real_projective_plane
gptkb:real_4-sphere
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gptkbp:is_orientable
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yes
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gptkbp:is_smooth
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yes
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gptkbp:notation
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gptkb:CP^2
[35m[1m[0m
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gptkbp:Picard_group
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Z
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gptkbp:points_are_equivalence_classes_of
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nonzero triples (z0, z1, z2) in C^3
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gptkbp:quotient_of
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C^3 \\ {0} by C*
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gptkbp:real_dimension
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4
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gptkbp:second_Betti_number
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1
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gptkbp:third_Betti_number
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0
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gptkbp:used_in
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gptkb:algebraic_geometry
gptkb:topology
differential geometry
complex geometry
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gptkbp:bfsParent
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gptkb:octonionic_projective_plane
gptkb:real_projective_plane
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gptkbp:bfsLayer
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6
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