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searching for Complex projective plane 20 found (84 total)

alternate case: complex projective plane

Complex affine space (2,538 words) [view diff] no match in snippet view article find links to article

over the complex affine plane but remain equivalent over the (complex) projective plane. Any complex vector space is an affine space: all one needs to

Line 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 projective

Max 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 {\displaystyle

Klara 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 problem

Quaternionic 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: 56–6

Margarethe 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 problem

Quantum 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–Study

Inverse 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 produce

Nef 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 the

Linear 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) and

Simple 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) Hyperbolic

Hopf 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-connected

Projective 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 space

Logarithmic 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,y

Homology (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 cobordism

Oval (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 is

Möbius 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/BF03026567

Algebraic 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 [m

Lane 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 &