ON PROJECTIVE MANIFOLDS SWEPT OUT BY CUBIC VARIETIES

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  • KIWAMU WATANABE
    Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan

説明

<jats:p> 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<jats:sup>1</jats:sup> × ℙ<jats:sup>2</jats:sup>. In the course of the proof, we classify projective manifolds of dimension five swept out by planes. </jats:p>

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