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Rationally connected varieties and fundamental groups

János Kollár
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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-Thélène.

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János Kollár. 2002-11-13. Rationally connected varieties and fundamental groups. https://arxiv.org/abs/math/0203174

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