×

Homomorphisms between Kähler groups. (English) Zbl 1221.32007

Cogolludo-Agustín, José Ignacio (ed.) et al., Topology of algebraic varieties and singularities. Invited papers of the conference in honor of Anatoly Libgober’s 60th birthday, Jaca, Spain, June 22–26, 2009. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Matemática Española (ISBN 978-0-8218-4890-6/pbk). Contemporary Mathematics 538, 95-111 (2011).
Kähler groups are fundamental groups of compact Kähler manifolds.
The author studies Kähler homomorphisms, namely those isomorphisms between Kähler groups coming from a holomorphic map. The main result consists of a splitting theorem which states that, if \(f:X\rightarrow Y\) is a proper connected holomorphic map from a Kähler manifold into a complex one, then the splitting obstruction \(e(\pi_1(f))\in H^2(\pi_1(Y),K/DK)\) is torsion, where \(K=\ker(\pi_1(f))\).
For the entire collection see [Zbl 1210.14004].

MSC:

32J27 Compact Kähler manifolds: generalizations, classification
57S25 Groups acting on specific manifolds
PDFBibTeX XMLCite
Full Text: arXiv