标题： 三维空间中$\Bbb P^5$的具有三维平面曲线族的三文治 显示英文标题

标题： Threefolds in $\Bbb P^5$ with a 3-dimensional family of plane curves

摘要： 给出了一类由平面整曲线组成的维数至少为三的族所覆盖的光滑三维流形$\Bbb P^5$的分类定理，这些平面整曲线的次数为$d\geq 2.$。证明了对于这样的三维流形$X$，有两种可能性： \item {(1)} $X$ 是超二次曲面中的任意三重体； \item {(2)} $d\leq 3$ 和 $X$要么是 Bordiga 曲面，要么是 Palatini 曲面。 显示英文摘要

摘要： A classification theorem is given of smooth threefolds of $\Bbb P^5$ covered by a family of dimension at least three of plane integral curves of degree $d\geq 2.$ It is shown that for such a threefold $X$ there are two possibilities: \item{(1)} $X$ is any threefold contained in a hyperquadric; \item{(2)} $d\leq 3$ and $X$ is either the Bordiga or the Palatini scroll.