English

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