English

Projected Gromov-Witten varieties in cominuscule spaces

Algebraic Geometry 2017-06-12 v2 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.1312.2468,
  title  = {Projected Gromov-Witten varieties in cominuscule spaces},
  author = {Anders S. Buch and Pierre-Emmanuel Chaput and Leonardo C. Mihalcea and Nicolas Perrin},
  journal= {arXiv preprint arXiv:1312.2468},
  year   = {2017}
}

Comments

13 pages

R2 v1 2026-06-22T02:23:48.186Z