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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2108.08620 |
| Etiquetas: |
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- 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.