The Lefschetz property for families of curves

2014/03/11 by Kollár, János
#14F35 #14J40 #14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1403.2670

Abstract

By the Lefschetz hyperplane theorem, if X is a smooth quasi-projective variety and C a general curve section of X then the fundamental group of C surjects onto the fundamental group of X. Here we consider when this conclusion holds for a general member of an arbitrary family of curves that covers X. The most interesting case is families of rational curves.

Related

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