Rationally connected varieties and fundamental groups
Algebraic Geometry
2007-05-23 v2
Abstract
Let U be an open subset of a unirational variety (or more generally of a separably rationally connected variety). We prove that there is rational curve C in U such that the fundamental group of C surjects onto the fundamental group of U. The proof improves the earlier proof (math.AG/0003138) and works in any characteristic. Much improved version, thanks to comments of Colliot-Th\'el\`ene.
Cite
@article{arxiv.math/0203174,
title = {Rationally connected varieties and fundamental groups},
author = {János Kollár},
journal= {arXiv preprint arXiv:math/0203174},
year = {2007}
}