Open Access
February 2015 Curve neighborhoods of Schubert varieties
Anders S. Buch, Leonardo C. Mihalcea
J. Differential Geom. 99(2): 255-283 (February 2015). DOI: 10.4310/jdg/1421415563


A previous result of the authors with Chaput and Perrin states that the closure of the union of all rational curves of fixed degree passing through a Schubert variety in a homogeneous space $G/P$ is again a Schubert variety. In this paper we identify this Schubert variety explicitly in terms of the Hecke product of Weyl group elements. We apply our result to give an explicit formula for any two-point Gromov-Witten invariant as well as a new proof of the quantum Chevalley formula and its equivariant generalization.We also recover a formula for the minimal degree of a rational curve between two given points in a cominuscule variety.


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Anders S. Buch. Leonardo C. Mihalcea. "Curve neighborhoods of Schubert varieties." J. Differential Geom. 99 (2) 255 - 283, February 2015.


Published: February 2015
First available in Project Euclid: 16 January 2015

zbMATH: 06423472
MathSciNet: MR3302040
Digital Object Identifier: 10.4310/jdg/1421415563

Rights: Copyright © 2015 Lehigh University

Vol.99 • No. 2 • February 2015
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