2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231467We show that for any minuscule or cominuscule homogeneous space X, the Gromov-Witten varieties of degree d curves passing through three general points of X are rational or empty for any d. Applying techniques of A. Buch and L. Mihalcea to constructions of the authors together with L. Manivel, we deduce that the equivariant K-theoretic three points Gromov-Witten invariants are equal to classical equivariant K-theoretic invariants on auxilliary spaces.19 pagesAlgebraic GeometryRepresentation Theory14M15, 14N35text