Quantum cohomology of [C^N/\mu_r]

TL;DR

This paper develops a new approach to compute genus-zero Gromov-Witten invariants for stacks like [C^N/μ_r] by constructing moduli spaces via root constructions and deriving explicit formulas and recursions.

Contribution

It introduces a novel construction of the moduli space of stable maps to Bμ_r using root constructions and provides explicit formulas for Chern classes and recursive relations for invariants.

Findings

Closed formula for total Chern class of μ_r-eigenspaces of the Hodge bundle

Linear recursions for all genus-zero Gromov-Witten invariants

Construction of moduli space via r-th root constructions

Abstract

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.