Belyi pairs in the critical filtrations of Hurwitz spaces

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  We are considering Hurwitz spaces stratified by the number of critical values.Belyi pairs constitute the zero-dimensional strata,and it is suggested to study them along with the higher-dimensional strata; in particular,a special attention will be paid to the one-dimensional strata(curves with functions having 4 critical values)for which the name FRIED NET is suggested.
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