Authors: R. Moschetti, G.P.Pirola
Abstract: We study the components of the Hurwitz scheme of ramified coverings of $\P^1$ with monodromy given by the alternating group $A_6$ 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 in \cite{FriedAlternating} for the $3$-cycles, we use as invariant the lifting to the Valentiner group, triple covering of $A_6$. We prove that the Hurwitz scheme has two irreducible components when the genus of the covering is greater than zero.
Link: arxiv.org/abs/1607.02844
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