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

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

1996-04-02

arxiv.org/abs/alg-geom/9604002v1

Mathematics

Algebraic Geometry

17 pages, to appear in Manuscripta Mathematica Plain TeX

Scientific paper

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.

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