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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2018

Projected Gromov-Witten varieties in cominuscule spaces

Résumé

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 projected Gromov-Witten varieties, which extends an earlier result of Knutson, Lam, and Speyer, and provides an alternative version of the ‘quantum equals classical’ theorem. Our proof uses that any projected Gromov-Witten variety in a cominuscule space is also a projected Richardson variety.

Dates et versions

hal-02102704 , version 1 (17-04-2019)

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Anders Skovsted Buch, Pierre-Emmanuel Chaput, Leonardo Constantin Mihalcea, Nicolas Perrin. Projected Gromov-Witten varieties in cominuscule spaces. Proceedings of the American Mathematical Society, 2018, 146, pp.3647-3660. ⟨10.1090/proc/13839⟩. ⟨hal-02102704⟩
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