Projected Gromov-Witten varieties in cominuscule spaces

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/PX = G/P. When XX is cominuscule we prove that the map from a related Gromov-Witten variety is cohomologically trivial. This implies that all (3-...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2018-09, Vol.146 (9), p.3647-3660
Main Authors: Buch, Anders S., Chaput, Pierre–Emmanuel, Mihalcea, Leonardo C., Perrin, Nicolas
Format: Article
Language:English
Subjects:
A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
Mathematics
Research article
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Summary: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/PX = G/P. When XX is cominuscule we prove that the map from a related Gromov-Witten variety is cohomologically trivial. This implies that all (3-point, genus zero) KK-theoretic Gromov-Witten invariants of XX 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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13839