Unramified Gromov-Witten and Gopakumar-Vafa invariants

Kim, Kresch and Oh defined unramified Gromov-Witten invariants. For a threefold, Pandharipande conjectured that they are equal to Gopakumar-Vafa invariants (BPS invariants) in the case of Fano classes and primitive Calabi-Yau classes. We prove the conjecture using a wall-crossing technique. This provides an algebro-geometric construction of Gopakumar-Vafa invariants in these cases.