Local Gromov–Witten invariants of blowups of Fano surfaces

In this paper, using the degeneration formula we obtain a blowup formula of local Gromov–Witten invariants of Fano surfaces. This formula makes it possible to compute the local Gromov–Witten invariants of non-toric Fano surfaces from toric Fano surfaces, such as del Pezzo surfaces. This formula also verified an expectation of Chiang–Klemm–Yau–Zaslow in Section 8.3 of Chiang et al. (1999) [7]