Kavli Affiliate: Todor Milanov
| First 5 Authors: Todor Milanov, Alexis Roquefeuil, , ,
| Summary:
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 $qto 1$, 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.
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