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In mathematics, a rational normal scroll is a ruled surface of degree n in projective space of dimension n + 1. Here "rational" means birational to projective space, "scroll" is an old term for ruled surface, and "normal" refers to projective normality (not normal schemes).
A non-degenerate irreducible surface of degree m – 1 in Pm is either a rational normal scroll or the Veronese surface.
Constructionedit
In projective space of dimension m + n + 1 choose two complementary linear subspaces of dimensions m > 0 and n > 0. Choose rational normal curves in these two linear subspaces, and choose an isomorphism φ between them. Then the rational normal surface consists of all lines joining the points x and φ(x). In the degenerate case when one of m or n is 0, the rational normal scroll becomes a cone over a rational normal curve. If m < n then the rational normal curve of degree m is uniquely determined by the rational normal scroll and is called the directrix of the scroll.
rational, normal, scroll, this, article, multiple, issues, please, help, improve, discuss, these, issues, talk, page, learn, when, remove, these, template, messages, this, article, relies, largely, entirely, single, source, relevant, discussion, found, talk, p. This article has multiple issues Please help improve it or discuss these issues on the talk page Learn how and when to remove these template messages This article relies largely or entirely on a single source Relevant discussion may be found on the talk page Please help improve this article by introducing citations to additional sources Find sources Rational normal scroll news newspapers books scholar JSTOR November 2021 This article includes a list of references related reading or external links but its sources remain unclear because it lacks inline citations Please help improve this article by introducing more precise citations November 2021 Learn how and when to remove this template message Learn how and when to remove this template message In mathematics a rational normal scroll is a ruled surface of degree n in projective space of dimension n 1 Here rational means birational to projective space scroll is an old term for ruled surface and normal refers to projective normality not normal schemes A non degenerate irreducible surface of degree m 1 in Pm is either a rational normal scroll or the Veronese surface Construction editIn projective space of dimension m n 1 choose two complementary linear subspaces of dimensions m gt 0 and n gt 0 Choose rational normal curves in these two linear subspaces and choose an isomorphism f between them Then the rational normal surface consists of all lines joining the points x and f x In the degenerate case when one of m or n is 0 the rational normal scroll becomes a cone over a rational normal curve If m lt n then the rational normal curve of degree m is uniquely determined by the rational normal scroll and is called the directrix of the scroll References editGriffiths Phillip Harris Joseph 1994 Principles of algebraic geometry Wiley Classics Library New York John Wiley amp Sons ISBN 978 0 471 05059 9 MR 1288523 Retrieved from https en wikipedia org w index php title Rational normal scroll amp oldid 1132871218, wikipedia, wiki, book, books, library,
