Gromov--Witten theory beyond maximal contacts
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911499356733440 |
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| author | Wang, Yu You, Fenglong |
| author_facet | Wang, Yu You, Fenglong |
| contents | Given a smooth projective variety $X$ and a smooth nef divisor $D$, we identify genus zero relative Gromov--Witten invariants of $(X,D)$ with $(n+1)$ relative markings with genus zero orbifold Gromov--Witten invariants of multi-root stacks over the $\mathbb P^1$-bundle $P:=\mathbb P(\mathcal O_X(-D)\oplus \mathcal O_X)$ with $n$ orbifold markings. This is a generalization of the local-relative correspondence beyond maximal contacts. Repeating this process, we identify genus zero relative Gromov--Witten invariants of ambient insertions with genus zero absolute Gromov--Witten invariants of toric bundles. We also present how this correspondence can be used to compute genus zero two-point relative Gromov--Witten invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17200 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gromov--Witten theory beyond maximal contacts Wang, Yu You, Fenglong Algebraic Geometry Given a smooth projective variety $X$ and a smooth nef divisor $D$, we identify genus zero relative Gromov--Witten invariants of $(X,D)$ with $(n+1)$ relative markings with genus zero orbifold Gromov--Witten invariants of multi-root stacks over the $\mathbb P^1$-bundle $P:=\mathbb P(\mathcal O_X(-D)\oplus \mathcal O_X)$ with $n$ orbifold markings. This is a generalization of the local-relative correspondence beyond maximal contacts. Repeating this process, we identify genus zero relative Gromov--Witten invariants of ambient insertions with genus zero absolute Gromov--Witten invariants of toric bundles. We also present how this correspondence can be used to compute genus zero two-point relative Gromov--Witten invariants. |
| title | Gromov--Witten theory beyond maximal contacts |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.17200 |