Local Gromov-Witten invariants of Blowups of Fano surfaces

TL;DR

This paper derives a blowup formula for local Gromov-Witten invariants of Fano surfaces, enabling computations for non-toric cases from toric surfaces and confirming a theoretical expectation.

Contribution

It introduces a new blowup formula for local Gromov-Witten invariants of Fano surfaces using degeneration techniques, expanding computational methods.

Findings

Formula allows computation of invariants for non-toric Fano surfaces from toric cases

Verifies the Chiang-Klemm-Yau-Zaslow expectation

Facilitates calculations for del Pezzo surfaces

Abstract

In this paper, using the degeneration formula we obtain a blowup formulae 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 form toric Fano surface, such as del Pezzo surfaces. This formula also verifed an expectation of Chiang-Klemm-Yau-Zaslow.