Refined floor diagrams relative to a conic and Caporaso-Harris type formula
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909798220431360 |
|---|---|
| author | Ding, Yanqiao Hu, Jianxun |
| author_facet | Ding, Yanqiao Hu, Jianxun |
| contents | We prove a $q$-refined correspondence theorem between higher genus relative Gromov-Witten invariants with a Lambda class $λ_{g-g'}$ insertion in the blow-up of $\mathbb{P}^2$ at $k$ points on a conic and the refined counts of genus $g'$ floor diagrams relative to a conic, after the change of variables $q=e^{iu}$. We provide a Caporaso-Harris type recursive formula for the refined counts of higher genus floor diagrams. As an application of the correspondence theorem, we propose a higher genus version of the BPS polynomials of del Pezzo surfaces of degree $\geq3$ and Hirzebruch surfaces, which generalize the higher genus Block-Göttsche polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refined floor diagrams relative to a conic and Caporaso-Harris type formula Ding, Yanqiao Hu, Jianxun Algebraic Geometry 14N35, 14T20 We prove a $q$-refined correspondence theorem between higher genus relative Gromov-Witten invariants with a Lambda class $λ_{g-g'}$ insertion in the blow-up of $\mathbb{P}^2$ at $k$ points on a conic and the refined counts of genus $g'$ floor diagrams relative to a conic, after the change of variables $q=e^{iu}$. We provide a Caporaso-Harris type recursive formula for the refined counts of higher genus floor diagrams. As an application of the correspondence theorem, we propose a higher genus version of the BPS polynomials of del Pezzo surfaces of degree $\geq3$ and Hirzebruch surfaces, which generalize the higher genus Block-Göttsche polynomials. |
| title | Refined floor diagrams relative to a conic and Caporaso-Harris type formula |
| topic | Algebraic Geometry 14N35, 14T20 |
| url | https://arxiv.org/abs/2509.06004 |