We introduce the different focal loci (focal points, planes and hyperplanes) of (n-1)-dimensional families (congruences) of lines in Pn and study their invariants, geometry and the relation among them. We also study some particular congruence’s 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.
Focal Loci in G(1,N) / E. Arrondo, M. Bertolini, C. Turrini. - In: THE ASIAN JOURNAL OF MATHEMATICS. - ISSN 1093-6106. - 9:4(2005), pp. 449-472.
Focal Loci in G(1,N)
M. BertoliniSecondo
;C. TurriniUltimo
2005
Abstract
We introduce the different focal loci (focal points, planes and hyperplanes) of (n-1)-dimensional families (congruences) of lines in Pn and study their invariants, geometry and the relation among them. We also study some particular congruence’s 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.
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