The Quantum Orbifold Cohomology of Weighted Projective Space

We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental’s heuristic argument, which relates small quantum cohomology to S-equivariant Floer cohomology of loop space, to weighted projective spaces and use this to conjecture an explicit formula for the small J-function, a generating function for certain genuszero Gromov–Witten invariants. We prove this conjecture using a method due to Bertram. We also obtain formulas for the small Jfunctions of weighted projective complete intersections satisfying a combinatorial condition; this condition naturally singles out the class of orbifolds with terminal singularities.