Weighted stable maps to [C^N/Z_r] and Gromov-Witten invariants
-- Charles Cadman, March 27, 2009

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I will describe joint work with Arend Bayer in which we compute
genus 0 orbifold Gromov-Witten invariants of [C^N/Z_r] for a
linear action of a cyclic group Z_r on C^N.  We use weighted stable maps in
an essential way. The outcome of our work is to encode the
total Chern class of the obstruction bundle into a family of
piecewise analytic functions from real tori into the real
cohomology of the moduli space of pointed stable curves of
genus 0.  We also have a combinatorial
technique for extracting the Gromov-Witten invariants from these
data.  We hope this work can be used to study the crepant
resolution conjecture for the orbifolds [C^N/Z_r].