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Fundamental Groups of Galois Closures of Generic Projections

Christian Liedtke
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Abstract

For the Galois closure $\Xgal$ of a generic projection from a surface $X$, it is believed that $π_1(\Xgal)$ gives rise to new invariants of $X$. However, in all examples this group is surprisingly simple. In this article, we offer an explanation for this phenomenon: We compute a quotient of $π_1(\Xgal)$ that depends on $π_1(X)$ and data from the generic projection only. In all known examples except one, this quotient is in fact isomorphic to $π_1(\Xgal)$. As a byproduct, we simplify part of the computations of Moishezon, Teicher and others.

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Christian Liedtke. 2008-06-09. Fundamental Groups of Galois Closures of Generic Projections. https://arxiv.org/abs/math/0505406

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