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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4109

Title: On Congruences of Linear Spaces of Order One
Authors: De Poi, Pietro
Mezzetti, Emilia
Keywords: Grassmannians
Congruences
Focal Locus
Fundamental Locus
Multisecant Lines
Issue Date: 2007
Publisher: EUT Edizioni Università di Trieste
Citation: 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.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (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.
URI: http://hdl.handle.net/10077/4109
ISSN: 0049-4704
MS Classification: 14M15
14J45
53A25
14N25
14M07
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.39 (2007)

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