Holomorphic anomaly equation for $({\mathbb P}^2,E)$ and the Nekrasov-Shatashvili limit of local ${\mathbb P}^2$

Abstract

We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$-insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D.

Keywords

• 14N35