Threefolds in ${\mathbb{P}}^5$ with a 3-dimensional family of plane curves

Abstract

A classification theorem is given of smooth threefolds of ${\mathbb{P}}^5$ covered by a family of dimension at least three of plane integral curves of degree $d\ge 2.$ 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)} $d\le 3$ and $X$ is either the Bordiga or the Palatini scroll.

arXiv comment17 pages, to appear in Manuscripta Mathematica Plain TeX

References in corpus (1)

• Projective varieties with many degenerate subvarieties