Cohomological restrictions on Kahler groups
Abstract
The number of the relations of a Kahler group is bounded below by the number of the generators and some geometric invariants of the corresponding compact Kahler manifold, like the irregularity, the Albanese dimension and the Albanese genera. Appropriate functions of the aforementioned geometric invariants are shown to be lower bounds for the Betti numbers of the Kahler group within the range, determined by the Albanese dimension.
Keywords
Cite
@article{arxiv.math/0105177,
title = {Cohomological restrictions on Kahler groups},
author = {Azniv Kasparian},
journal= {arXiv preprint arXiv:math/0105177},
year = {2007}
}
Comments
The author apologizes for claiming incorrectly in the previous version that a theorem of Remmert and Van de Ven, used by Amoros is wrong. As pointed out by Prof. Amoros, the counterexample, constructed there, is fake since the exterior product of a vector space with itself has nontrivial kernel and does not admit a projectivization. Both, Remmert and Van de Ven's Theorem and Amoros' results are perfectly accurate. The note conststs of 11 pages