Fundamental Groups of Galois Closures of Generic Projections
نویسنده
چکیده
For the Galois closure Xgal of a generic projection from a surface X, it is believed that π1(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 π1(Xgal) that depends on π1(X) and data from the generic projection only. In all known examples, this quotient is in fact isomorphic to π1(Xgal). As a byproduct, we simplify the computations of Moishezon, Teicher and others.
منابع مشابه
On Fundamental Groups of Galois Closures of Generic Projections
We study the fundamental group of the Galois closure Xgal of a generic projection from a surface X. Originally, it was believed that π1(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 π1(Xgal) that depends on π1(X) and data from the generic projection only....
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