Varieties with ample cotangent bundle
Varieties with ample cotangent bundle
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具有充足余切束的品种
作者：
O. Debarre
本文的目的是提供构造具有充足余切丛的光滑射影复簇的方法。我们证明，维度为 n 的复阿贝尔簇中至少 n/2 个足够充足的一般超曲面的交集具有充足的余切丛。我们还讨论了射影空间中完全相交的类似问题。最后，我们提出了博戈莫洛夫未发表的结果，该结果指出，足够多具有大余切丛的光滑射影簇的乘积的小尺寸一般线性部分具有充足的余切丛。
The aim of this article is to provide methods for constructing smooth projective complex varieties with ample cotangent bundle. We prove that the intersection of at least n/2 sufficiently ample general hypersurfaces in a complex abelian variety of dimension n has ample cotangent bundle. We also discuss analogous questions for complete intersections in the projective space. Finally, we present an unpublished result of Bogomolov which states that a general linear section of small dimension of a product of sufficiently many smooth projective varieties with big cotangent bundle has ample cotangent bundle.