Rationally connected manifolds and semipositivity of the Ricci curvature
Rationally connected manifolds and semipositivity of the Ricci curvature
复制标题
有理连通流形和里奇曲率的半正性
DOI：
10.1017/cbo9781107416000.006
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
T. Peternell
中科院分区：
文献类型：
--
作者：
F. Campana;J. Demailly;T. Peternell
本文建立了具有半正反正则丛的紧致Kahler流形的一个结构定理。在有限根覆盖下，证明了这类流形作为Ricci平坦簇和有理连通流形的乘积全纯等距分裂。证明是基于一个合理的连通流形的特征，通过不存在某些扭曲的逆变张量积的切丛，沿着与广义holonomy原则的伪有效线丛。一个关键的因素是uniruledness的特点的性质，anticanonical丛是不是pseudoeffective。
This work establishes a structure theorem for compact Kahler manifolds with semipositive anticanonical bundle. Up to finite etale cover, it is proved that such manifolds split holomorphically and isometrically as a product of Ricci flat varieties and of rationally connected manifolds. The proof is based on a characterization of rationally connected manifolds through the non existence of certain twisted contravariant tensor products of the tangent bundle, along with a generalized holonomy principle for pseudoeffective line bundles. A crucial ingredient for this is the characterization of uniruledness by the property that the anticanonical bundle is not pseudoeffective.