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

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.