Fibred K"ahler and quasi-projective Groups
| dc.creator | Catanese, Fabrizio | |
| dc.date | 2003-07-04 | |
| dc.date.accessioned | 2026-07-07T04:59:26Z | |
| dc.date.available | 2026-07-07T04:59:26Z | |
| dc.description | 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. | |
| dc.description | 16 pages, to appear in Advances in Geometry (2003), Volume in honour of the 80-th birthday of Adriano Barlotti | |
| dc.identifier | https://arxiv.org/abs/math/0307065 | |
| dc.identifier | http://arxiv.org/abs/math/0307065 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67981 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D05, 14J80, 32J25 | |
| dc.title | Fibred K"ahler and quasi-projective Groups | |
| dc.type | text |