纤维K“ahler群与拟投射群
Fibred K"ahler and quasi-projective Groups
摘要：
给出了一个新的定理，给出了紧致Kähler流形的基本群$π_1(X)$到亏格为$g \geq 2$的紧致Riemann曲面的基本群$Π_g$上的满射由全纯映射导出的几个充要条件.例如，它足以使内核被并行生成。作为推论，我们推导出一个群$G$的限制，它适合于一个正合序列$ 1 \ra H \ra G \ra Π_g \ra 1$，其中$H$是双生成的，是一个紧凑的Kähler流形的基本群。由于鲍尔和阿拉普拉的卡斯泰尔诺沃德弗朗基斯定理的准投射的情况下（更一般地说，到Zorbiki开集的紧凑凯勒流形），我们首先扩展到非紧的情况下以前的结果。最后给出了由极大秩的真全纯映射所围成的拟射影曲面的一个拓扑刻画。
英文摘要：
We formulate a new theorem giving several necessary and sufficient conditions in order that a surjection of the fundamental group $π_1(X)$ of a compact Kähler manifold onto the fundamental group $Π_g$ of a compact Riemann surface of genus $g \geq 2$ be induced by a holomorphic map. For instance, it suffices that the kernel be finitely generated. We derive as a corollary a restriction for a group $G$, fitting into an exact sequence $ 1 \ra H \ra G \ra Π_g \ra 1$, where $H$ is finitely generated, to be the fundamental group of a compact Kähler manifold. Thanks to the extension by Bauer and Arapura of the Castelnuovo de Franchis theorem to the quasi-projective case (more generally, to Zariski open sets of compact Kähler manifolds) we first extend the previous result to the non compact case. We are finally able to give a topological characterization of quasi-projective surfaces which are fibred over a (quasi-projective) curve by a proper holomorphic map of maximal rank.
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