Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle
Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle
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DOI：
10.1007/s00208-014-1083-x
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发表时间：
2015-04-01
影响因子：
1.4
通讯作者：
Watanabe, Kiwamu
中科院分区：
文献类型：
--
作者：
Munoz, Roberto;Occhetta, Gianluca;Watanabe, Kiwamu
具有nef切线束的Fano流形，如果它具有与完全标志流形相同的初等收缩，则它是标志型的。在本文中，我们根据Dynkin图的收缩的数值性质，提出了一种将Dynkin图与任何这样的图联系起来的方法。然后我们证明了这是一个半简单李群的Dynkin图。作为一个应用，我们证明了Campana-Peternell猜想在为标志型流形时成立，其Dynkin图为，即为P-n中线性子空间的完全标志的集合。
A Fano manifold with nef tangent bundle is of Flag-Type if it has the same kind of elementary contractions as a complete flag manifold. In this paper we present a method to associate a Dynkin diagram with any such , based on the numerical properties of its contractions. We then show that is the Dynkin diagram of a semisimple Lie group. As an application we prove that Campana-Peternell conjecture holds when is a Flag-Type manifold whose Dynkin diagram is , i.e. we show that is the variety of complete flags of linear subspaces in P-n.