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Line Congruences of Low Order

Arrondo Esteban, Enrique (2002) Line Congruences of Low Order. Milan Journal of Mathematics, 70 (1). pp. 223-243. ISSN 1424-9286

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Abstract

A line congruence is an irreducible subvariety of dimension n−1 in the Grassmannian of lines in Pn. There are two numerical invariants associated to a line congruence: the order, which is the number of lines passing through a general point of Pn, and the class, which is the number of lines of the congruence contained in a general hyperplaneH and meeting a general line inH. The paper reviews the classification of line congruences of order 0 and 1, and then gives some new results online congruences of order 2 in P3, which is a work in progress. The last section states some open questions.


Item Type:Article
Uncontrolled Keywords:Grassmannians, Schubert varieties
Subjects:Sciences > Mathematics > Algebra
ID Code:12484
Deposited On:28 Mar 2011 10:56
Last Modified:06 Feb 2014 09:25

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