We study the stack B h,g,n of uniform cyclic covers of degree n between smooth curves of genus h and g and, for h ≫ g, present it as an open substack of a vector bundle over the universal Jacobian stack of Mg. We use this description to compute the integral Picard group of B h,g,n , showing that it is generated by tautological classes of B h,g,n .
We construct virtual fundamental classes of Artin stacks over a Dedekind
domain endowed with a perfect obstruction theory.Comment: 12 pages, comments welcom
We computeétale cohomology groups H í et (X, Gm) in several cases, where X is a smooth tame Deligne-Mumford stack of dimension 1 over an algebraically closed field. We have complete results for orbicurves (and, more generally, for twisted nodal curves) and in the case all stabilizers are cyclic; we give partial results and examples in the general case. In particular, we show that if the stabilizers are abelian then H 2 et (X, Gm) does not depend on X but only on the underlying orbicurve and on the generic stabilizer. arXiv:1008.0538v2 [math.AG]
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