2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77514This is an expository article about the recent results on the relation between the naturality problem of quantum cohomology and birational geometry. We give a short survey on Li-Ruan's results. Some conjecture-proposals are discussed.A minor revision. A better description of log stable map and correction of typoAlgebraic GeometryHigh Energy Physics - Theorytext