Rationally connected varieties and fundamental groups

Details Rationally connected varieties and fundamental groups Rationally connected varieties and fundamental groups

2002-03-18

arxiv.org/abs/math/0203174v2

Mathematics

Algebraic Geometry

Scientific paper

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-Th\'el\`ene.

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