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arXiv · 1404.5763

The ambiguity index of an equipped finite group

F. A. Bogomolov·Vik. S. Kulikov
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Abstract

In \cite{Ku0}, the ambiguity index $a_{(G,O)}$ was introduced for each equipped finite group $(G,O)$. It is equal to the number of connected components of a Hurwitz space parametrizing coverings of a projective line with Galois group $G$ assuming that all local monodromies belong to conjugacy classes $O$ in $G$ and the number of branch points is greater than some constant. We prove in this article that the ambiguity index can be identified with the size of a generalization of so called Bogomolov multiplier (\cite{Kun1}, see also \cite{BO87}) and hence can be easily computed for many pairs $(G,O)$.

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F. A. Bogomolov, Vik. S. Kulikov. 2014-04-23. The ambiguity index of an equipped finite group. https://arxiv.org/abs/1404.5763

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