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Fundamental groups of Galois closures of generic projections


Author: Christian Liedtke
Journal: Trans. Amer. Math. Soc. 362 (2010), 2167-2188
MSC (2000): Primary 14E20, 14J29
DOI: https://doi.org/10.1090/S0002-9947-09-04941-1
Published electronically: October 19, 2009
MathSciNet review: 2574891
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Abstract: For the Galois closure $ X_{{\rm gal}}$ of a generic projection from a surface $ X$, it is believed that $ \pi_1(X_{{\rm gal}})$ 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 $ \pi_1(X_{{\rm gal}})$ that depends on $ \pi_1(X)$ and data from the generic projection only. In all known examples, this quotient is in fact isomorphic to $ \pi_1(X_{{\rm gal}})$. As a byproduct, we simplify the computations of Moishezon, Teicher and others.


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Additional Information

Christian Liedtke
Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
Address at time of publication: Department of Mathematics, Stanford University, 450 Serra Mall, Stanford, California 94305
Email: liedtke@math.uni-duesseldorf.de, liedtke@math.stanford.edu

DOI: https://doi.org/10.1090/S0002-9947-09-04941-1
Received by editor(s): November 2, 2005
Received by editor(s) in revised form: June 9, 2008
Published electronically: October 19, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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