Polynomial P^1-orbifolds and their Mirror Model

Abstract:

We compute Gromov-Witten theory of P^1-orbifolds with positive Euler characteristic by exhibiting a mirror model from singularity theory which generalizes the space of Laurent polynomials. Moreover we obtain mirror symmetry with a third source of Frobenius manifolds, namely extended affine Weyl groups of type A, D, E. We also give a constructive procedure to compute the Frobenius (genus 0 Gromov-Witten) potential which makes use of Symplectic Field Theory.