2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161093In this paper, we study some vanishing identities for Gromov-Witten invariants conjectured by K. Liu and H. Xu. We will prove these conjectures in the case that the summation range is large compare to genus. In fact, in such cases, we can obtain a vanishing identity which is stronger than their conjectures. Moreover we will also prove their conjectures in low genus cases.15 pages, LaTex file. Added more cases to Theorem 0.3Differential GeometryAlgebraic Geometrytext