K-theoretic Gromov-Witten invariants of line degrees on flag varieties
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917775674441728 |
|---|---|
| author | Buch, Anders S. Chen, Linda Xu, Weihong |
| author_facet | Buch, Anders S. Chen, Linda Xu, Weihong |
| contents | A homology class $d \in H_2(X)$ of a complex flag variety $X = G/P$ is called a line degree if the moduli space $\overline{M}_{0,0}(X,d)$ of 0-pointed stable maps to $X$ of degree $d$ is also a flag variety $G/P'$. We prove a quantum equals classical formula stating that any $n$-pointed (equivariant, K-theoretic, genus zero) Gromov-Witten invariant of line degree on $X$ is equal to a classical intersection number computed on the flag variety $G/P'$. We also prove an $n$-pointed analogue of the Peterson comparison formula stating that these invariants coincide with Gromov-Witten invariants of the variety of complete flags $G/B$. Our formulas make it straightforward to compute the big quantum K-theory ring of $X$ modulo degrees larger than line degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-theoretic Gromov-Witten invariants of line degrees on flag varieties Buch, Anders S. Chen, Linda Xu, Weihong Algebraic Geometry 14N35 (Primary) 19E08, 14N15, 14M15 (Secondary) A homology class $d \in H_2(X)$ of a complex flag variety $X = G/P$ is called a line degree if the moduli space $\overline{M}_{0,0}(X,d)$ of 0-pointed stable maps to $X$ of degree $d$ is also a flag variety $G/P'$. We prove a quantum equals classical formula stating that any $n$-pointed (equivariant, K-theoretic, genus zero) Gromov-Witten invariant of line degree on $X$ is equal to a classical intersection number computed on the flag variety $G/P'$. We also prove an $n$-pointed analogue of the Peterson comparison formula stating that these invariants coincide with Gromov-Witten invariants of the variety of complete flags $G/B$. Our formulas make it straightforward to compute the big quantum K-theory ring of $X$ modulo degrees larger than line degrees. |
| title | K-theoretic Gromov-Witten invariants of line degrees on flag varieties |
| topic | Algebraic Geometry 14N35 (Primary) 19E08, 14N15, 14M15 (Secondary) |
| url | https://arxiv.org/abs/2409.09580 |