2013/12/09 by Anders Skovsted Buch, Buch, Anders S., Pierre–Emmanuel Chaput +5 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · doi:10.48550/arxiv.1312.2468
openalex publication_date 2013/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A projected Gromov-Witten variety is the union of all rational curves of fixed degree that meet two opposite Schubert varieties in a homogeneous space X = G/P. When X is cominuscule we prove that the map from a related Gromov-Witten variety is cohomologically trivial. This implies that all (3 point, genus zero) K-theoretic Gromov-Witten invariants of X are determined by the projected Gromov-Witten varieties, which extends an earlier result of Knutson, Lam, and Speyer. Our proof uses that any projected Gromov-Witten variety in a cominuscule space is also a projected Richardson variety.