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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2108.08620 |
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| _version_ | 1866910402792652800 |
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| author | Milanov, Todor Roquefeuil, Alexis |
| author_facet | Milanov, Todor Roquefeuil, Alexis |
| contents | For a smooth projective variety whose anti-canonical bundle is nef, we prove confluence of the small $K$-theoretic $J$-function, i.e., after rescaling appropriately the Novikov variables, the small $K$-theoretic $J$-function has a limit when $q\to 1$, which coincides with the small cohomological $J$-function. Furthermore, in the case of a Fano toric manifold $X$ of Picard rank 2, we prove the $K$-theoretic version of an identity due to Iritani that compares the $I$-function of the toric manifold and the oscillatory integral of the toric mirror. In particular, our confluence result yields a new proof of Iritani's identity in the case of a toric manifold of Picard rank 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_08620 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Confluence in quantum K-theory of weak Fano manifolds and q-oscillatory integrals for toric manifolds Milanov, Todor Roquefeuil, Alexis Algebraic Geometry 14N35 (Primary), 35Q53, 39A45 (Secondary) For a smooth projective variety whose anti-canonical bundle is nef, we prove confluence of the small $K$-theoretic $J$-function, i.e., after rescaling appropriately the Novikov variables, the small $K$-theoretic $J$-function has a limit when $q\to 1$, which coincides with the small cohomological $J$-function. Furthermore, in the case of a Fano toric manifold $X$ of Picard rank 2, we prove the $K$-theoretic version of an identity due to Iritani that compares the $I$-function of the toric manifold and the oscillatory integral of the toric mirror. In particular, our confluence result yields a new proof of Iritani's identity in the case of a toric manifold of Picard rank 2. |
| title | Confluence in quantum K-theory of weak Fano manifolds and q-oscillatory integrals for toric manifolds |
| topic | Algebraic Geometry 14N35 (Primary), 35Q53, 39A45 (Secondary) |
| url | https://arxiv.org/abs/2108.08620 |