English

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.

Keywords

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

R2 v1 2026-07-22T16:31:49.391Z