Homomorphisms between Kaehler groups

Details Homomorphisms between Kaehler groups Homomorphisms between Kaehler groups

2009-08-06

arxiv.org/abs/0908.0929v1

Mathematics

Algebraic Geometry

17 pages, latex, expanded talk at conference in Jaca for Anatoly Libgober

Scientific paper

This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a homomorphism induced by a holomorphic map between these types of manifolds. Some obstructions for a homomorphism to be Kaehler are discussed. Among these is the main result on the vanishing of a certain cohomology class associated to such map. This is reduced to the decomposition theorem for perverse sheaves suitably extended to Kaehler orbifolds.

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