Fundamental groups of rationally connected varieties

János Kollár

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Fundamental groups of rationally connected varieties

János Kollár

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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-Thélène 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 Teichmüller group.

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BibTeX RIS

János Kollár. 2000-03-23. Fundamental groups of rationally connected varieties. https://arxiv.org/abs/math/0003138

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