Hurwitz spaces and liftings to the Valentiner group |
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Authors: | Riccardo Moschetti Gian Pietro Pirola |
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Affiliation: | 1. Department of Mathematics and Natural Sciences, University of Stavanger, NO-4036 Stavanger, Norway;2. Dipartimento di Matematica, Università di Pavia, Italy |
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Abstract: | We study the components of the Hurwitz scheme of ramified coverings of with monodromy given by the alternating group 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 . 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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Keywords: | 14D05 14H30 14Q05 |
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