Orbifold quantum cohomology of weighted projective spaces

In this article, we prove the following results. We show a mirror theorem: the Frobenius manifold associated to the orbifold quantum cohomology of weighted projective spaces is isomorphic to the one attached to a specific Laurent polynomial. We show a reconstruction theorem; that is, we can reconstruct in an algorithmic way the full genus 0 Gromov-Witten potential from the 3-point invariants.