Curve neighborhoods of Schubert varieties
By Anders Skovsted Buch, Leonardo Constantin Mihalcea. 2013
68 citations recorded by the source corpus.
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 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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/81fe616d9e3d90fe627412fd6ad487299f4691bb
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
- Matthew J. Samuel
- Anders Skovsted Buch
- Alexander Yong
- Leonardo Constantin Mihalcea
- Damir Yeliussizov
- Harry Tamvakis
- Andrew Kresch
- Hugh Thomas
In Mathematical Physics
Citations in the corpus
- K-theory of minuscule varieties (2013, background): “The following tableau is a Pieri tableau of type B with range [1, 6] = {1, 2, 3, 4, 5, 6}.”