Congruences of Lines with one-dimensional focal locus
In this article we obtain the classification of the congruences of lines with one-dimensional focal locus. It turns out that one can restrict to study the case of $\mathbb{P}^3$.
math.AG↗
arXiv subjects
Pietro De Poi
Publications and source records attributed to Pietro De Poi.
On first order Congruences of Lines in $\mathbb{P}^4$ with irreducible fundamental Surface
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 $F$.
math.AG↗
Threefolds of P^5 with one apparent quadruple point
In this article we classify all the smooth threefolds of P^5 with an apparent quadruple point provided that the family of its 4-secant lines is an irreducible (first order) congruence. This is sufficient to conclude the classification of all the smooth codimension two varieties of P^n with one apparent (n-1)-point and with irreducible family of (n-1)-secant lines.
math.AG↗