complex projective lineの例文

• The M鯾ius transformations are the projective transformations of the complex projective line.
• Examples include the real projective line, the complex projective line, and the projective line over quaternions.
• The Riemann sphere is one example of a complex algebraic manifold, since it is the complex projective line.
• Nevanlinna theory addresses the question of the distribution of values of a holomorphic curve in the complex projective line.
• The complex analog of the real projective line is the complex projective line; that is, the Riemann sphere.
• In the case of a complex projective line, or the Riemann sphere, these transformation are known as M鯾ius transformations.
• A distinction between the terms arose when the distinction was clarified between the real projective plane and the complex projective line.
• In quantum mechanics, points on the complex projective line are natural values for photon relativistic model for the celestial sphere.
• For example, any line ( or smooth conic ) in the complex projective plane is biholomorphic to the complex projective line.
• The analogue for the complex projective plane is a'line'at infinity that is ( naturally ) a complex projective line.
• The formula given for above defines an explicit diffeomorphism between the complex projective line and the ordinary-sphere in-dimensional space.
• The middle dimension 2 is accounted for by the homology class of the complex projective line, or Riemann sphere, lying in the plane.
• For instance, M鯾ius transformations ( transformations of the complex projective line, or Riemann sphere ) are affine ( transformations of the complex plane ) if and only if they fix the point at infinity.
• The flag variety may be identified with the complex projective line with homogeneous coordinates and the space of the global sections of the line bundle is identified with the space of homogeneous polynomials of degree on.
• Just as the Riemann sphere needs a north pole point at infinity to close up the complex projective line, so a line at infinity succeeds in closing up the plane of dual numbers to a cylinder.
• So that, for example, the projectivization of two-dimensional complex Hilbert space ( the space describing one qubit ) is the complex projective line \ mathbb { C } P ^ { 1 }.
• A family of concentric circles centered at a single focus " C " forms a special case of a hyperbolic pencil, in which the other focus is the point at infinity of the complex projective line.
• Since there are no non-trivial field automorphisms of the real number field, all the collineations are homographies in the real projective plane ., however due to the field automorphism complex conjugation, not all collineations of the complex projective line are homographies.
• For example, in a map from a connected complex surface to the complex projective line, a generic fiber is a smooth Riemann surface of some fixed genus g and, generically, there will be isolated points in the target whose preimages are nodal curves.
• A geometric interpretation of the fibration may be obtained using the complex projective line,, which is defined to be the set of all complex one-dimensional quotient of by the equivalence relation which identifies with for any nonzero complex number " ? ".