Article ID Journal Published Year Pages File Type
5772838 Journal of Pure and Applied Algebra 2018 20 Pages PDF
Abstract
We study the components of the Hurwitz scheme of ramified coverings of P1 with monodromy given by the alternating group A6 and elements in the conjugacy class of product of two disjoint cycles. In order to detect the connected components of the Hurwitz scheme, inspired by the case of the spin structures studied by Fried for the 3-cycles, we use as invariant the lifting to the Valentiner group, a triple covering of A6. We prove that the Hurwitz scheme has two irreducible components when the genus of the covering is greater than zero, in accordance with the asymptotic solution found by Bogomolov and Kulikov.
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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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