ON PROJECTIVE MANIFOLDS SWEPT OUT BY CUBIC VARIETIES
ON PROJECTIVE MANIFOLDS SWEPT OUT BY CUBIC VARIETIES
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DOI：
10.1142/s0129167x12500589
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发表时间：
2010-10
影响因子：
0.6
通讯作者：
Kiwamu Watanabe
中科院分区：
文献类型：
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作者：
Kiwamu Watanabe
我们研究了被三次簇扫出的嵌入射影流形的结构。我们证明了如果一个嵌入的射影流形被高维光滑的三次超曲面扫出，那么它允许一个极值收缩，它是一个线性射影丛或一个三次纤维化。作为应用，我们给出了光滑三次超曲面的一个刻划。我们还分类了被塞格雷三重流形的副本1 × 2扫过的维数至多为5的嵌入射影流形。在证明过程中，我们对被平面扫掠的五维射影流形进行了分类。
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 × ℙ2. In the course of the proof, we classify projective manifolds of dimension five swept out by planes.