On contractions of extremal rays of Fano manifolds.
On contractions of extremal rays of Fano manifolds.
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关于 Fano 流形的极值射线的收缩。
DOI：
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发表时间：
1991
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通讯作者：
J. Wiśniewski
中科院分区：
文献类型：
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作者：
J. Wiśniewski
如果其反规范除数 Kx 充足，则复数上的平滑变体 X 称为 Fano。这篇文章的目的是收集一些关于极值射线收缩（Mori 理论）的结果，这些结果从描述维度 ^ 4 的 Fano 流形的角度来看很有趣。该理论已成功用于维度 3，请参阅 [MM]，并且希望类似的方法可以在更高维度中以某种方式起作用。此外，法诺流形的极值射线收缩可以被视为一般射线收缩的测试场。尽管光滑簇射线的收缩在 2 维和 3 维中已被很好地理解，请参阅 [M2]，但在更高维度中仍然知之甚少，请参阅 [An]、[Bei] 和 [Ka]。本文第 l 节和第 2 节的大部分结果适用于一般设置，即不需要假设
A smooth variety X over complex numbers is called Fano if its anticanonical divisor — Kx is ample. The purpose of this note is to collect some results on contractions of extremal rays (Mori theory) which are interesting from the point of describing Fano manifolds of dimension ^ 4. The theory has been successfully used in dimension 3, see [MM], and there is some hope that a similar approach may work somehow in higher dimensions. Furthermore, contractions of extremal rays of Fano manifolds can be treated äs testing grounds for contractions of rays in general. Although contractions of rays of smooth varieties are well understood in dimensions 2 and 3, see [M2], there are still few things known in higher dimensions, see [An], [Bei] and [Ka]. Most of the results of sections l and 2 of the present paper are applicable in a general set-up, i.e. do not need the assumption on ampleness of