Fundamental group and pluridifferentials on compact K\"ahler manifolds
Algebraic Geometry
2015-11-06 v2
Abstract
A compact K\"ahler manifold is shown to be simply-connected if its `symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective connected holomorphic map between connected complex manifolds induces an isomorphism of fundamental groups if its smooth fibres are as above, and if the domain is K\"ahler.
Keywords
Cite
@article{arxiv.1510.07922,
title = {Fundamental group and pluridifferentials on compact K\"ahler manifolds},
author = {Yohan Brunebarbe and Frédéric Campana},
journal= {arXiv preprint arXiv:1510.07922},
year = {2015}
}
Comments
v2: 10 pages; minor changes