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arXiv · 2610.39127

The inverse local-relative correspondence and the Nekrasov--Shatashvili vanishing blowup equation

Jianjun Fu·Shuai Guo·Qingsheng Zhang
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Abstract

We prove the Nekrasov--Shatashvili vanishing blowup equation for the local Gromov--Witten theory of smooth weak del Pezzo surfaces, by identifying its unique formal solution with the inverse of the local-relative correspondence. We construct this inverse through an associative set-partition convolution and establish the identification using Zagier's recursion for the Bloch--Okounkov $n$-point function. The proof applies in all genera and includes non-toric surfaces.

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Jianjun Fu, Shuai Guo, Qingsheng Zhang. 2026-10-29. The inverse local-relative correspondence and the Nekrasov--Shatashvili vanishing blowup equation. https://arxiv.org/abs/2610.39127

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