On First Order Congruences of Lines in $\mathbb{P}^4$ with Generically Non-reduced Fundamental Surface

Details On First Order Congruences of Lines in $\mathbb{P}^4$ with Generically Non-reduced Fundamental Surface On First Order Congruences of Lines in $\mathbb{P}^4$ with Generically Non-reduced Fundamental Surface

2004-07-20

arxiv.org/abs/math/0407341v3

Mathematics

Algebraic Geometry

10 pages, AMS-LaTeX; to appear in ``The Asian Journal of Mathematics''

Scientific paper

In this article we obtain a complete description of the congruences of lines
in $\p^4$ of order one provided that the fundamental surface $F$ is non-reduced
(and possibly reducible) at one of its generic points, and their classification
under the hypothesis that $(F)_{\red}$ is smooth.

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