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arXiv · 1403.2670

The Lefschetz property for families of curves

János Kollár
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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.

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János Kollár. 2014-03-11. The Lefschetz property for families of curves. https://arxiv.org/abs/1403.2670

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