不含非平凡子簇的紧致Kähler三维流形
Compact Kähler 3-manifolds without non-trivial subvarieties
摘要：
我们证明了任何不含非平凡复子簇的紧致Kähler三维流形都是环面。这是一个非常特殊的情况下，一般猜想的结构'简单的流形'，中央双纯分类的紧凑凯勒流形。证明如下从布鲁内拉伪有效性定理，结合基本结果的萧和第二作者的勒龙数封闭的正（1，1）-电流，并与硬莱夫谢茨定理的一个版本的伪有效线丛，由于武越和Demailly-Peternell-Schneider。类似地，我们证明了一个正规紧的、Kähler的、具有终端奇点和nef典范丛的三维解析空间是一个简单非投射环面的循环商，如果它不带有效因子。这是完成紧致Kähler 3-折叠双半纯分类的关键一步
英文摘要：
We prove that any compact Kähler 3-dimensional manifold which has no non-trivial complex subvarieties is a torus. This is a very special case of a general conjecture on the structure of 'simple manifolds', central in the bimeromorphic classification of compact Kähler manifolds. The proof follows from the Brunella pseudo-effectivity theorem, combined with fundamental results of Siu and of the second author on the Lelong numbers of closed positive (1,1)-currents, and with a version of the hard Lefschetz theorem for pseudo-effective line bundles, due to Takegoshi and Demailly-Peternell-Schneider. In a similar vein, we show that a normal compact and Kähler 3-dimensional analytic space with terminal singularities and nef canonical bundle is a cyclic quotient of a simple non-projective torus if it carries no effective divisor. This is a crucial step to complete the bimeromorphic classification of compact Kähler 3-folds
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