Fibred Kähler and quasi-projective groups.

By F. Catanese. 2003

49 citations recorded by the source corpus.

We formulate a new theorem giving several necessary and sufficient conditions in order that a surjection of the fundamental group πι^) of a compact Kahler manifold onto the fundamental group Π^ of a compact Riemann surface of genus g ^ 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 -» H -* G —> U g —> 1, where H is finitely generated, to be the fundamental group of a compact Kahler 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 Kahler manifolds) we first extend the previous result to the non-compact case. We are finally able to give a topo- logical characterization of quasi-projective surfaces which are fibred over a (quasi-projective) curve by a proper holomorphic map of maximal rank, and we extend the previous restriction to the monodromy of any fibration onto a curve.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/69929c233e5344c0b4136ab0c43c3fb6a45f4738

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Topological methods in moduli theory (2014, result): “First of all, by the results of Siu and others ([101,106,344,345], Theorem 5.”
Topological methods in algebraic geometry (2015, result): “First of all, by the results of Siu and others ([31, 84, 85], [34, Theorem 5.”