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On Congruences of Linear Spaces of Order One
De Poi, Pietro
Mezzetti, Emilia
2007
Abstract
After presenting the main notions and results about
congruences of k-planes, we dwell upon congruences of lines,
mainly of order one. We survey the classification results in the
projective spaces of dimension 3 and 4, which are almost complete,
and the (partial) results and some conjectures in higher
dimension. Finally we present some new results, in particular a
degree bound for varieties with one apparent double point, a new
class of examples with focal locus of high degree, and some general
results about the classification of first order congruences of
lines in $\mathbb P^4$ with reducible focal surface.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (2007)
Publisher
EUT Edizioni Università di Trieste
Source
Pietro De Poi, Emilia Mezzetti, "On Congruences of Linear Spaces of Order One”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 39 (2007), pp. 177-229.
Languages
en
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