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

Pietro De Poi
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Abstract

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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Pietro De Poi. 2007-04-29. On First Order Congruences of Lines in $\mathbb{P}^4$ with Generically Non-reduced Fundamental Surface. https://arxiv.org/abs/math/0407341

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