English

Quantum Schubert calculus for smooth Schubert divisors of $F\ell_n$

Algebraic Geometry 2025-09-23 v1

Abstract

We propose to study the quantum Schubert calculus for Schubert varieties, and investigate the smooth Schubert divisors X of the complete flag variety Fl_n. We provide a Borel-type ring presentation of the quantum cohomology of X. We derive the quantum Chevalley formula for X by geometric arguments. We also show that the quantum Schubert polynomials for X are the same as that for Fl_n introduced by Fomin, Gelfand and Postnikov.

Keywords

Cite

@article{arxiv.2509.17857,
  title  = {Quantum Schubert calculus for smooth Schubert divisors of $F\ell_n$},
  author = {Changzheng Li and Jiayu Song and Rui Xiong and Mingzhi Yang},
  journal= {arXiv preprint arXiv:2509.17857},
  year   = {2025}
}

Comments

27 pages