Confluence in quantum K-theory of weak Fano manifolds and q-oscillatory integrals for toric manifolds
Confluence in quantum K-theory of weak Fano manifolds and q-oscillatory integrals for toric manifolds
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弱 Fano 流形的量子 K 理论与环面流形的 q 振荡积分的汇合
DOI：
10.1016/j.aim.2022.108682
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发表时间：
2022
影响因子：
1.7
通讯作者：
Todor Milanov and Alexis Roquefeuil
中科院分区：
文献类型：
--
作者：
Itoh;Jin-ichi;榎本一之;伊藤仁一;清原一吉;Todor Milanov and Alexis Roquefeuil
对于反标准丛为nef的光滑射影簇，证明了小K理论J函数的收敛性，即适当地重新标度Novikov变量后，当q→ 1时，小K理论J函数有极限，这与小上同调J函数一致.此外，在一个Fano复曲面流形皮卡秩2的情况下，我们证明了K理论版本的身份由于Iritani比较的I-函数的复曲面流形和振荡积分的复曲面镜。特别是，我们的合流结果产生一个新的证明Iritani的身份的情况下，复曲面流形的皮卡秩2。
For a smooth projective variety whose anti-canonical bundle is nef, we prove confluence of the small K-theoretic J-function, ie, 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.