Mathematics – Algebraic Geometry
Scientific paper
2004-07-20
Mathematics
Algebraic Geometry
18 pages, AMS-LaTeX; submitted
Scientific paper
In this article we study congruences of lines in $\mathbb{P}^n$, and in
particular of order one. After giving general results, we obtain a complete
classification in the case of $\mathbb{P}^4$ in which the fundamental surface
$F$ is in fact a variety-i.e. it is integral-and the congruence is the
irreducible set of the trisecant lines of $F$.
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