Quantum Schubert calculus for smooth Schubert divisors of $F\ell_n$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911168515276800 |
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| author | Li, Changzheng Song, Jiayu Xiong, Rui Yang, Mingzhi |
| author_facet | Li, Changzheng Song, Jiayu Xiong, Rui Yang, Mingzhi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Schubert calculus for smooth Schubert divisors of $F\ell_n$ Li, Changzheng Song, Jiayu Xiong, Rui Yang, Mingzhi Algebraic Geometry 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. |
| title | Quantum Schubert calculus for smooth Schubert divisors of $F\ell_n$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.17857 |