论文标题
Kähler的辫子群是什么时候？
When are braid groups of manifolds Kähler?
论文作者
论文摘要
在某个时候，我们表明一个纯净的Artin Braid群体不是Kähler，即，这不是紧凑的Kähler歧管的基本群体。这使用了Bressler，Ramachandran和作者的结果，Kähler群体不能太“大”。这里的目的是研究其他编织群体的Kählerness问题。主要结果是，除了一些琐碎的例外，黎曼表面的纯辫子至少是2条链的纯辫子。在某些情况下，证明使用了先前的策略，因为其他策略会扮演事先对Beauville-Catanese-Siu定理的后果建立的辫子群体的某些同源性能。复杂维度2或更多的投影歧管的辫子组显示给一个投影歧管的基本组，因此显示了Kähler。
Sometime ago, we showed that a pure Artin braid group is not Kähler, i.e. it is not the fundamental group of a compact Kähler manifold. This used a result of Bressler, Ramachandran and the author that Kähler groups cannot be too "big". The goal here is to study the problem of Kählerness for other braid groups. The main result is that, with some trivial exceptions, the pure braid group of a Riemann surface with at least 2 strands is never Kähler. In some cases the proof uses the previous strategy, for others it plays off some homological properties of braid groups established beforehand against consequences of the Beauville-Catanese-Siu theorem. The braid group of a projective manifold of complex dimension 2 or more is shown to the fundamental group of a projective manifold, and hence Kähler.
