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Classification of smooth congruences with a fundamental curve

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Arrondo Esteban, Enrique and Bertolini, Marina and Turrini, Cristina (1994) Classification of smooth congruences with a fundamental curve. In Projective geometry with applications. A collection of 15 research papers. Lect. Notes Pure Appl. Math (166). Dekker, New York, pp. 43-56. ISBN 0-8247-9278-5

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Abstract

A congruence of lines is a (n−1)-dimensional family of lines in Pn (over C), i.e. a variety Y of dimension (and hence of codimension) n − 1 in the Grassmannian Gr(1, Pn). A
fundamental curve for Y is a curve C Pn which meets all the lines of Y . In this paper the authors classify all smooth congruences with fundamental curve C generalizing
a paper by E. Arrondo and M. Gross [Manuscr. 79, No. 3-4, 283-298 (1993; Zbl 0803.14019)], where the case n = 3 was treated. An explicit construction for all possible congruences that they found is also given.


Item Type:Book Section
Uncontrolled Keywords:Congruence of lines; Grassmannian; fundamental curve
Subjects:Sciences > Mathematics > Algebra
ID Code:21039
Deposited On:24 Apr 2013 14:11
Last Modified:07 Feb 2014 10:24

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