Threefolds in \Bbb P⁵ with a 3-dimensional family of plane curves

1996/04/02 by Emilia Mezzetti, Mezzetti, Emilia, Dario Portelli +1
Mathematics · #14J30 14M07 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #alg-geom #math.AG #msc:14J30 #msc:14M07

paper · pdf · doi:10.48550/arxiv.alg-geom/9604002

17 pages, to appear in Manuscripta Mathematica Plain TeX

arxiv created 1996/04/02 · openalex publication_date 1996/04/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classification theorem is given of smooth threefolds of \Bbb P⁵ covered by a family of dimension at least three of plane integral curves of degree d≥ 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≤ 3 and X is either the Bordiga or the Palatini scroll.

Citations

• Projective varieties with many degenerate subvarieties

Related

• On the quadratic normality and the triple curve of three dimensional subvarieties of \mathbb P⁵
• On smooth rational threefolds of P⁵ with rational non-special hyperplane section
• On quadrisecant lines of threefolds in P⁵
• On threefolds covered by lines
• On surfaces in P⁴ and 3-folds in P⁵