Quantum cohomology of [C^N/μ_r]

Abstract

We give a construction of the moduli space of stable maps to the classifying stack Bμ_r of a cyclic group by a sequence of r-th root constructions on M_{0, n}. We prove a closed formula for the total Chern class of μ_r-eigenspaces of the Hodge bundle, and thus of the obstruction bundle of the genus zero Gromov-Witten theory of stacks of the form [C^N/μ_r]. We deduce linear recursions for all genus-zero Gromov-Witten invariants.

33 pages, 1 figure; v2: expository changes, references updated