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 P^4 with reducible focal surface.
On congruences of linear spaces of order one
MEZZETTI, EMILIA
2007-01-01
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 P^4 with reducible focal surface.File in questo prodotto:
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