Curve neighborhoods of schubert varieties

Anders S. Buch, Leonardo C. Mihalcea

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)255-283
Number of pages29
JournalJournal of Differential Geometry
Volume99
Issue number2
DOIs
StatePublished - Feb 1 2015

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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