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Focal loci in G(1,N)

Arrondo Esteban, Enrique and Bertolini, Marina and Turrini, Cristina (2005) Focal loci in G(1,N). Asian journal of mathematics, 9 (4). pp. 449-472. ISSN 1093-6106

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We introduce the different focal loci (focal points, planes and hyperplanes) of (n - 1)-dimensional families (congruences) of lines in P-n and study their invariants, geometry and the relation among them. We also study some particular congruences whose focal loci have special behaviour, namely (n - 1)-secant lines to an (n - 2)-fold and (n - 1)-tangent lines to a hypersurface. In case n = 4 we also give, under some smoothness assumptions, a classification result for these congruences.

Item Type:Article
Uncontrolled Keywords:Focal locus; congruence; Grassmannian of lines
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14822

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