complex projective planeの例文

• This torus may be embedded in the complex projective plane by means of the map
• The triangle is the "'toric base "'of the complex projective plane.
• In the complex projective plane the non-degenerate conics can not be distinguished from one another.
• Rational surface means surface birational to the complex projective plane "'P "'2.
• In the complex projective plane all polarities are hyperbolic but in the real projective plane only some are.
• For example, the complex projective plane "'CP "'2 may be represented by three complex coordinates satisfying
• For example, any line ( or smooth conic ) in the complex projective plane is biholomorphic to the complex projective line.
• Originally, the " Klein quartic " referred specifically to the subset of the complex projective plane defined by freely on by isometries.
• The analogue for the complex projective plane is a'line'at infinity that is ( naturally ) a complex projective line.
• Max Noether and Castelnuovo showed that the Cremona group of birational automorphisms of the complex projective plane is generated by the " quadratic transformation"
• There are many other projective planes, both infinite, such as the complex projective plane, and finite, such as the Fano plane.
• The nontrivial homotopy groups of the complex projective plane are \ pi _ 2 = \ pi _ 5 = \ mathbb { Z }.
• In the geometry of a complex projective plane, the circular points at infinity seem to be all that is needed to define which curves are circles.
• Using the theory of elliptic functions, it can be shown that elliptic curves defined over the complex numbers correspond to embeddings of the torus into the complex projective plane.
• Each curve in the pencil passes through the nine points of the complex projective plane whose homogeneous coordinates are some permutation of 0,  1, and a cube root of unity.
• It is not realizable in the Euclidean plane but is realizable in the complex projective plane as the nine inflection points of an elliptic curve with the 12 lines incident with triples of these.
• This would imply the previous result because algebraic curves ( complex dimension 1, real dimension 2 ) are symplectic surfaces within the complex projective plane, which is a symplectic 4-manifold.
• Assuming that \ Sigma has nonnegative self intersection number this was generalized to K鋒ler manifolds ( an example being the complex projective plane ) by Taubes, also using the then-new Seiberg Witten invariants.
• It was disproved for positive first Chern classes by Yau, who observed that the complex projective plane blown up at 2 points has no K鋒ler & ndash; Einstein metric and so is a counterexample.
• In algebraic geometry, the Calabi conjecture implies the Miyaoka Yau inequality on Chern numbers of surfaces, a characterization of the complex projective plane and quotients of the two-dimensional complex unit ball, an important class of Shimura varieties.