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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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Cite

BibTeXRIS
BibTeX
@misc{fu2026inverse,
  title = {{The inverse local-relative correspondence and the Nekrasov--Shatashvili vanishing blowup equation}},
  author = {Jianjun Fu and Shuai Guo and Qingsheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39127},
  eprint = {2610.39127},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39127},
}
RIS
TY  - UNPB
TI  - The inverse local-relative correspondence and the Nekrasov--Shatashvili vanishing blowup equation
AU  - Jianjun Fu
AU  - Shuai Guo
AU  - Qingsheng Zhang
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39127
UR  - https://arxiv.org/abs/2610.39127
AB  - 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.
ER  -