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

Emilia Mezzetti·Dario Portelli
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Abstract

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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Emilia Mezzetti, Dario Portelli. 1996-04-02. Threefolds in $\Bbb P^5$ with a 3-dimensional family of plane curves. https://arxiv.org/abs/alg-geom/9604002

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