2010/10/12 by Kiwamu Watanabe, Watanabe, Kiwamu
Mathematics · #14E30 (Secondary) #14J40 #14M99 #14N99 (Primary) 14D99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #math.AG #msc:14D99 #msc:14E30 #msc:14J40 #msc:14M99 #msc:14N99
paper · pdf · doi:10.48550/arxiv.1010.2300
18 pages, v2: title slightly changed, improved exposition, simplified the proof
openalex publication_date 2010/10/12 · arxiv created 2011/11/01 · arxiv updated 2011/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study structures of embedded projective manifolds swept out by cubic varieties. We show if an embedded projective manifold is swept out by high-dimensional smooth cubic hypersurfaces, then it admits an extremal contraction which is a linear projective bundle or a cubic fibration. As an application, we give a characterization of smooth cubic hypersurfaces. We also classify embedded projective manifolds of dimension at most five swept out by copies of the Segre threefold P1\timesP2. In the course of the proof, we classify projective manifolds of dimension five swept out by planes.