On quadrisecant lines of threefolds in P⁵

2001/12/07 by Emilia Mezzetti, Mezzetti, Emilia
Mathematics · #14J30 #14J70 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:14J30 #msc:14J70

paper · pdf · doi:10.48550/arxiv.math/0112075

Plain Tex, 12 pages

arxiv created 2001/12/07 · openalex publication_date 2001/12/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study smooth threefolds of the projective space of dimension 5 whose quadrisecant lines don't fill up the space. We give a complete classification of those threefolds X whose only quadrisecant lines are the lines contained in X. Then we prove that, if X admits "true" quadrisecant lines, but they don't fill up the space, then either X is contained in a cubic hypersurface, or it contains a family of dimension at least two of plane curves of degree at least four.

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