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

Emilia Mezzetti; Dario Portelli

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

alg-geom 2008-02-03 v1 Algebraic Geometry

Authors: Emilia Mezzetti , Dario Portelli

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.

Keywords

threefolds $\mathbb{P}^5$ plane curves Bordiga scroll Palatini scroll

Cite

@article{arxiv.alg-geom/9604002,
  title  = {Threefolds in $\Bbb P^5$ with a 3-dimensional family of plane curves},
  author = {Emilia Mezzetti and Dario Portelli},
  journal= {arXiv preprint arXiv:alg-geom/9604002},
  year   = {2008}
}

Comments

17 pages, to appear in Manuscripta Mathematica Plain TeX

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

Abstract

Keywords

Cite

Comments

Related papers