projective line


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projective line

[prə′jek·tiv ′līn]
(mathematics)
The line obtained from the stereographic projection of the circle.
References in periodicals archive ?
(i) [F.sub.E] [equivalent to] {[[0].sub.E], [[1].sub.E], [[[infinity]].sub.E]} for projective frames of the real projective line P[R.sup.1], and
Then, X is either a projective line bundle over [bar.X] or the direct product of [bar.X] and a fiber of [[phi].sub.R].
(i) So F = [[theta].sub.u] ([V.sub.2]), [V.sub.2] [subset] [V.sub.3], where the projective line L = [PV.sub.2] is of kind [[LAMBDA].sub.3], with line pattern (0,3,1,0).
Coverage includes a guide to closure operations in commutative algebra, a survey of test ideals, finite-dimensional vector spaces with Frobenius action, finiteness and homological conditions in commutative group rings, regular pullbacks, noetherian rings without finite normalization, Krull dimension of polynomial and power series rings, the projective line over the integers, on zero divisor graphs, and a closer look at non-unique factorization via atomic decay and strong atoms.
A line in P is given by an equation {(x, y, z)|ax + by + cz = 0}, that is, a projective line corresponds to a plane in [F.sup.3] containing the origin.
His condition is as follows: if each projective line has at least three points of intersection with hyperplanes in H, then [P.sup.n](C) - [absolute value of H] is Brody hyperbolic.
The projective line [P.sup.1.sub.K] over K is defined as the quotient space ([K.sup.2]\{0})/ ~ where ~ is the equivalence relation defined by: ([z.sub.0], [z.sub.1]) ~ ([w.sub.0], [w.sub.1]) if there exists a non-zero element c in K such that ([z.sub.0], [z.sub.1]) = (c X [w.sub.0], c X [w.sub.j]).
Topics of the 13 papers include products and powers of linear codes under component wise multiplication, the geometry of efficient arithmetic on elliptic curves, 2-2-2 isogenics between Jacobians of hyperelliptic curves, a point counting algorithm for cyclic covers of the projective line, genetics of polynomials over local fields, and smooth embeddings for the Suzuki and Ree curves.
over the regular bipyramid over Q is a direct product with the projective line [P.sub.1] [??] [X.sub.[-1,1]].
We project from a projective line intersecting X in two points x and y onto a 3-dimensional space [GAMMA] skew to this line.
Potential theory and dynamics on the Berkovich projective line.
An edge with its two vertices is a combinatorial projective line over [F.sub.1], and more generally, any subset of vertices together with the induced graph structure defines a linear subspace.