Fundamental groups of rationally connected varieties

2000/03/23 by János Kollár, Kollár, János · 1 citation
Mathematics · #14F35 #14H15 (Secondary) #14J45 (Primary) 14E20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E20 #msc:14F35 #msc:14H15 #msc:14J45

paper · pdf · doi:10.48550/arxiv.math/0003138

12 pages, LaTeX

arxiv created 2000/03/23 · arxiv updated 2009/11/30

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.

Cited by

• Mayer--Vietoris sequences for complexes of tori

Related

• Rationally connected varieties and fundamental groups
• The Lefschetz property for families of curves
• Toward the structure of fibered fundamental groups of projective varieties
• Fundamental groups of proper varieties are finitely presented
• Galois actions on fundamental groups of curves and the cycle C-C^-