Publication: Line Congruences of Low Order
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Publication Date
2002-09
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Birkhäuser
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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.