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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 |
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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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