Projected Gromov-Witten varieties in cominuscule spaces

TL;DR

This paper studies projected Gromov-Witten varieties in cominuscule spaces, proving their cohomological triviality and showing they determine all 3-point genus zero K-theoretic invariants, extending prior results.

Contribution

It establishes the cohomological triviality of related Gromov-Witten maps in cominuscule spaces and links these varieties to projected Richardson varieties, advancing understanding of Gromov-Witten invariants.

Findings

Map from Gromov-Witten variety is cohomologically trivial in cominuscule spaces

All 3-point genus zero K-theoretic invariants are determined by projected Gromov-Witten varieties

Projected Gromov-Witten varieties are also projected Richardson varieties

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.