The Spin Gromov-Witten/Hurwitz correspondence for $\mathbb{P}^1$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866909736066088960 |
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| author | Giacchetto, Alessandro Kramer, Reinier Lewański, Danilo Sauvaget, Adrien |
| author_facet | Giacchetto, Alessandro Kramer, Reinier Lewański, Danilo Sauvaget, Adrien |
| contents | We study the spin Gromov-Witten (GW) theory of $\mathbb{P}^1$. Using the standard torus action on $\mathbb{P}^1$, we prove that the associated equivariant potential can be expressed by means of operator formalism and satisfies the 2-BKP hierarchy. As a consequence of this result, we prove the spin analogue of the GW/Hurwitz correspondence of Okounkov-Pandharipande for $\mathbb{P}^1$, which was conjectured by J. Lee. Finally, we prove that this correspondence for a general target spin curve follows from a conjectural degeneration formula for spin GW invariants that holds in virtual dimension 0. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_03259 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Spin Gromov-Witten/Hurwitz correspondence for $\mathbb{P}^1$ Giacchetto, Alessandro Kramer, Reinier Lewański, Danilo Sauvaget, Adrien Algebraic Geometry Mathematical Physics 14N35, 14N10, 14H10, 14H70, 37K10, 37K20, 53D45 We study the spin Gromov-Witten (GW) theory of $\mathbb{P}^1$. Using the standard torus action on $\mathbb{P}^1$, we prove that the associated equivariant potential can be expressed by means of operator formalism and satisfies the 2-BKP hierarchy. As a consequence of this result, we prove the spin analogue of the GW/Hurwitz correspondence of Okounkov-Pandharipande for $\mathbb{P}^1$, which was conjectured by J. Lee. Finally, we prove that this correspondence for a general target spin curve follows from a conjectural degeneration formula for spin GW invariants that holds in virtual dimension 0. |
| title | The Spin Gromov-Witten/Hurwitz correspondence for $\mathbb{P}^1$ |
| topic | Algebraic Geometry Mathematical Physics 14N35, 14N10, 14H10, 14H70, 37K10, 37K20, 53D45 |
| url | https://arxiv.org/abs/2208.03259 |