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We prove a formula computing the Gromov-Witten invariants of genus zero with three marked points of the resolution of the transversal -singularity of the weighted projective space using the theory of deformations of surfaces with -singularities. We use this result to check Ruan’s conjecture for the stack .
In the space of degree polynomials, the hypersurfaces defined by the existence of a cycle of period and multiplier are known to be contained in the bifurcation locus. We prove that these hypersurfaces equidistribute the bifurcation current. This is a new result, even for the space of quadratic polynomials.