- projective hyperplane
- мат. проективная гиперплоскость
Большой англо-русский и русско-английский словарь. 2001.
projective hyperplane
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Hyperplane — A hyperplane is a concept in geometry. It is a higher dimensional generalization of the concepts of a line in Euclidean plane geometry and a plane in 3 dimensional Euclidean geometry. The most familiar kinds of hyperplane are affine and linear… … Wikipedia
Hyperplane at infinity — In mathematics, in particular projective geometry, the hyperplane at infinity, also called the ideal hyperplane, is an ( n −1) dimensional projective space added to an n dimensional affine space A, such as the real affine n space mathbb{R}^n , in … Wikipedia
Hyperplane section — In mathematics, a hyperplane section of a subset X of projective space P n is the intersection of X with some hyperplane H mdash; in other words we look at the subset X H of those elements x of X that satisfy the single linear condition L = 0… … Wikipedia
Projective space — In mathematics a projective space is a set of elements constructed from a vector space such that a distinct element of the projective space consists of all non zero vectors which are equal up to a multiplication by a non zero scalar. A formal… … Wikipedia
Projective frame — In the mathematical field of projective geometry, a projective frame is an ordered collection of points in projective space which can be used as reference points to describe any other point in that space. For example: * Given three distinct… … Wikipedia
Complex projective space — The Riemann sphere, the one dimensional complex projective space, i.e. the complex projective line. In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a … Wikipedia
Quadric (projective geometry) — In projective geometry a quadric is the set of points of a projective space where a certain quadratic form on the homogeneous coordinates becomes zero. It may also be defined as the set of all points that lie on their dual hyperplanes, under some … Wikipedia
Duality (projective geometry) — A striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this metamathematical concept. There are two approaches to the subject of … Wikipedia
Lefschetz hyperplane theorem — In mathematics, the Lefschetz hyperplane theorem states that a hyperplane section W of a non singular complex algebraic variety V , in complex projective space, inherits most of its algebraic topology from V . This allows certain geometrical… … Wikipedia
Reciprocity (projective geometry) — A reciprocity is a collineation from a projective space onto its dual space, taking points to hyperplanes (and vice versa) and preserving incidence.If it can be represented as a homography, it is called a correlation … Wikipedia
Ample line bundle — In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold M into projective space. An ample line bundle is one such that some positive power is very ample. Globally… … Wikipedia
