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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. 4356. ISBN 0824792785

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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. 34, 283298 (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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