Fundamental groups of galois closures of generic projections

Christian Liedtke

doi:10.1090/S0002-9947-09-04941-1

Fundamental groups of galois closures of generic projections

Christian Liedtke

Heinrich-Heine-University
Stanford University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

For the Galois closure X_gal of a generic projection from a surface X, it is believed that pi;1(X_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 π1(X_gal)that depends on π1(X) and data from the generic projection only. In all known examples, this quotient is in fact isomorphic to π1(X_gal). As a byproduct, we simplify the computations of Moishezon, Teicher and others.

Original language	English
Pages (from-to)	2167-2188
Number of pages	22
Journal	Transactions of the American Mathematical Society
Volume	362
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9947-09-04941-1
State	Published - Apr 2010
Externally published	Yes

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10.1090/S0002-9947-09-04941-1

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Fundamental groups of galois closures of generic projections

Abstract

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