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Complex affine space
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over the complex affine plane but remain equivalent over the (complex) projective plane. Any complex vector space is an affine space: all one needs toLine at infinity (711 words) [view diff] exact match in snippet view article find links to article
that they intersect at the line at infinity. The analogue for the complex projective plane is a 'line' at infinity that is (naturally) a complex projectiveMax Noether (650 words) [view diff] exact match in snippet view article find links to article
showed that the Cremona group of birational automorphisms of the complex projective plane is generated by the "quadratic transformation" [x,y,z] ↦ [1/x,Homogeneous coordinates (3,958 words) [view diff] exact match in snippet view article find links to article
The homogeneous form for the equation of a circle in the real or complex projective plane is x 2 + y 2 + 2 a x z + 2 b y z + c z 2 = 0 {\displaystyleKlara Löbenstein (520 words) [view diff] exact match in snippet view article find links to article
sixteenth problem concerned the topology of algebraic curves in the complex projective plane; as a difficult special case in his formulation of the problemQuaternionic projective space (1,245 words) [view diff] case mismatch in snippet view article find links to article
JSTOR 2373152. Arnol'd, V.I. (1999). "Relatives of the Quotient of the Complex Projective Plane by the Complex Conjugation". Tr. Mat. Inst. Steklova. 224: 56–6Margarethe Kahn (1,200 words) [view diff] exact match in snippet view article find links to article
sixteenth problem concerned the topology of algebraic curves in the complex projective plane; as a difficult special case in his formulation of the problemQuantum cohomology (1,800 words) [view diff] exact match in snippet view article find links to article
this intersection information for all classes A. Let X be the complex projective plane with its standard symplectic form (corresponding to the Fubini–StudyInverse curve (2,405 words) [view diff] exact match in snippet view article find links to article
circular points, (1, ±i, 0), when considered as a curve in the complex projective plane. In general, inversion with respect to an arbitrary curve may produceNef line bundle (2,039 words) [view diff] exact match in snippet view article find links to article
conjecture would give more. Example: Let X be the blow-up of the complex projective plane P 2 {\displaystyle \mathbb {P} ^{2}} at a point p. Let H be theLinear system of divisors (2,910 words) [view diff] exact match in snippet view article find links to article
common intersection, but given two (nondegenerate) conics in the complex projective plane, they intersect in four points (counting with multiplicity) andSimple Lie group (2,384 words) [view diff] exact match in snippet view article find links to article
Hermitian, quasi-split, quaternionic Complex hyperbolic plane Complex projective plane 1 4 10 Sp(2) = Spin(5), SO5(ℝ) Compact 10 SO4,1(ℝ), Sp2,2(ℝ) HyperbolicHopf conjecture (2,287 words) [view diff] exact match in snippet view article find links to article
present, the 4-sphere S 4 {\displaystyle \mathbb {S} ^{4}} and the complex projective plane C P 2 {\displaystyle \mathbb {CP} ^{2}} are the only simply-connectedProjective space (5,670 words) [view diff] exact match in snippet view article find links to article
genus of a plane algebraic curve from its singularities in the complex projective plane. So a projective variety is the set of points in a projective spaceLogarithmic form (2,984 words) [view diff] exact match in snippet view article find links to article
For an explicit example, consider an elliptic curve D in the complex projective plane P 2 = { [ x , y , z ] } {\displaystyle \mathbf {P} ^{2}=\{[x,yHomology (mathematics) (8,215 words) [view diff] exact match in snippet view article
real projective plane R P 2 {\displaystyle \mathbb {RP} ^{2}} and complex projective plane C P 2 {\displaystyle \mathbb {CP} ^{2}} have nontrivial cobordismOval (projective plane) (4,186 words) [view diff] exact match in snippet view article
the following simple criteria holds: 5. Any closed oval of the complex projective plane is a conic. An oval in a finite projective plane of order q isMöbius strip (9,639 words) [view diff] exact match in snippet view article find links to article
MR 2008500. Kühnel, W.; Banchoff, T. F. (1983). "The 9-vertex complex projective plane" (PDF). The Mathematical Intelligencer. 5 (3): 11–22. doi:10.1007/BF03026567Algebraic curve (7,993 words) [view diff] exact match in snippet view article find links to article
_{P},} where the sum is taken over all singular points P of the complex projective plane curve. It is called the genus formula. Assign the invariants [mLane P. Hughston (4,067 words) [view diff] case mismatch in snippet view article find links to article
L. P. Hughston & S. M. Salamon (2016) Surveying Points in the Complex Projective Plane, Advances in Mathematics, Vol 286, pp 1017–1052. D. C. Brody &