Curve neighborhoods of Schubert varieties
Abstract
A previous result of the authors with Chaput and Perrin states that 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 twopoint GromovWitten 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2013
 DOI:
 10.48550/arXiv.1303.6013
 arXiv:
 arXiv:1303.6013
 Bibcode:
 2013arXiv1303.6013B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics
 EPrint:
 24 pages, 1 figure, 1 table