Abstract
We study orbifold Gromov–Witten invariants of the r-th root stack XD,r with a pair of mid-ages when r is sufficiently large. We prove that genus g invariants with a pair of mid-ages ka/r and 1−ka/r are polynomials in ka and the kai-coefficients are polynomials in r with degree bounded by 2g. Moreover, genus zero invariants with a pair of mid-ages are independent of the choice of mid-ages. As an application, we obtain an identity for relative Gromov–Witten theory which can be viewed as a modified version of the usual loop axiom.
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