On projective manifolds swept out by cubic varieties

Details On projective manifolds swept out by cubic varieties On projective manifolds swept out by cubic varieties

2010-10-12

arxiv.org/abs/1010.2300v3

Mathematics

Algebraic Geometry

18 pages, v2: title slightly changed, improved exposition, simplified the proof

Scientific paper

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 P^1\timesP^2. In the course of the proof, we classify projective manifolds of dimension five swept out by planes.

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