Irrational pencils and Betti numbers
Geometric Topology
2023-03-31 v3 Algebraic Geometry
Group Theory
Abstract
We study irrational pencils with isolated critical points on compact aspherical complex manifolds. We prove that if the set of critical points is nonempty, the homology of the kernel of the morphism induced by the pencil on fundamental groups is not finitely generated. This generalizes a result by Dimca, Papadima and Suciu. By considering self-products of the Cartwright-Steger surface, this allows us to build new examples of smooth projective varieties whose fundamental group has a non-finitely generated homology.
Keywords
Cite
@article{arxiv.2006.09566,
title = {Irrational pencils and Betti numbers},
author = {Francisco Nicolás and Pierre Py},
journal= {arXiv preprint arXiv:2006.09566},
year = {2023}
}
Comments
10 pages, 1 figure, v3: this is the final version, accepted in Annales de la Facult\'e des Sciences de Toulouse