Abstract
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→1, which coincides with the small cohomological J-function. Furthermore, in the case of a Fano toric manifold 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.
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