Quantum cohomology of [C^N/μ_r]

Details Quantum cohomology of [C^N/μ_r] Quantum cohomology of [C^N/μ_r]

2007-05-15

arxiv.org/abs/0705.2160v2

Compos. Math., 2010, 146, 1291-1322

Mathematics

Algebraic Geometry

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

Scientific paper

10.1112/S0010437X10004793

We give a construction of the moduli space of stable maps to the classifying stack B\mu_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 \mu_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/\mu_r]. We deduce linear recursions for all genus-zero Gromov-Witten invariants.

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