Invariance of Quantum Rings under Ordinary Flops (journée sur les invariants de Gromov-Witten)

For ordinary flops over a smooth base, we determine the defect of the cup product under the canonical correspondence and show that it is corrected by the small quantum product attached to the extremal ray. If the flop is of splitting type, the big quantum cohomology ring is also shown to be invariant after an analytic continuation in the Kähler moduli space.