Fundamental groups of rationally connected varieties
Algebraic Geometry
2007-05-23 v1
Abstract
Let U be an open subset of a unirational 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. As a consequence we obtain new proofs of the theorems of Harbater and Colliot-Th\'el\`ene on Galois covers and torsors over the p-adic line. We also obtain examples of pencils of curves of genus <14 whose monodromy group is the full Teichm\"uller group.
Cite
@article{arxiv.math/0003138,
title = {Fundamental groups of rationally connected varieties},
author = {János Kollár},
journal= {arXiv preprint arXiv:math/0003138},
year = {2007}
}
Comments
12 pages, LaTeX