Fundamental groups of rationally connected varieties

Details Fundamental groups of rationally connected varieties Fundamental groups of rationally connected varieties

2000-03-23

arxiv.org/abs/math/0003138v1

Mathematics

Algebraic Geometry

12 pages, LaTeX

Scientific paper

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.

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