Higher genus Gromov-Witten invariants from projective bundles on smooth log Calabi-Yau pairs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916862856527872 |
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| author | Zhou, Benjamin |
| author_facet | Zhou, Benjamin |
| contents | Let $(X,E)$ be a smooth log Calabi-Yau pair consisting of a smooth Fano surface $X$ and a smooth anticanonical divisor $E$. We obtain certain higher genus local Gromov-Witten invariants from the projectivization of the canonical bundle $Z := \mathbb{P}(K_X \oplus \mathcal{O}_X)$, using the degeneration formula for stable log maps [KLR]. We evaluate an invariant in the degeneration using the relationship between $q$-refined tropical curve counting and logarithmic Gromov-Witten theory with $λ_g$-insertion [Bou]. As a corollary, we use flops to prove a blow up formula for higher genus invariants of $Z$. Additionally assuming $X$ is toric, we prove an all-genus correspondence between open invariants of an outer Aganagic-Vafa brane $L \subset K_X$ and closed invariants of $Z$ that generalizes a genus-0 open-closed equality of [Cha] to all-genus, by using an argument in [GRZZ]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher genus Gromov-Witten invariants from projective bundles on smooth log Calabi-Yau pairs Zhou, Benjamin Algebraic Geometry Mathematical Physics Symplectic Geometry Let $(X,E)$ be a smooth log Calabi-Yau pair consisting of a smooth Fano surface $X$ and a smooth anticanonical divisor $E$. We obtain certain higher genus local Gromov-Witten invariants from the projectivization of the canonical bundle $Z := \mathbb{P}(K_X \oplus \mathcal{O}_X)$, using the degeneration formula for stable log maps [KLR]. We evaluate an invariant in the degeneration using the relationship between $q$-refined tropical curve counting and logarithmic Gromov-Witten theory with $λ_g$-insertion [Bou]. As a corollary, we use flops to prove a blow up formula for higher genus invariants of $Z$. Additionally assuming $X$ is toric, we prove an all-genus correspondence between open invariants of an outer Aganagic-Vafa brane $L \subset K_X$ and closed invariants of $Z$ that generalizes a genus-0 open-closed equality of [Cha] to all-genus, by using an argument in [GRZZ]. |
| title | Higher genus Gromov-Witten invariants from projective bundles on smooth log Calabi-Yau pairs |
| topic | Algebraic Geometry Mathematical Physics Symplectic Geometry |
| url | https://arxiv.org/abs/2503.17713 |