Mock modularity of log Gromov--Witten Invariants: the mirror to $\mathbb{P}^2$
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915785075589120 |
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| author | Argüz, Hülya |
| author_facet | Argüz, Hülya |
| contents | We study modularity properties of generating series of logarithmic Gromov-Witten invariants of elliptic fibrations relative to singular fibers. Motivated by predictions from Vafa-Witten theory, we conjecture that such generating series are mock modular forms. We prove this conjecture for a large class of invariants of the rational elliptic surface mirror to $\mathbb{P}^2$, relative to a cycle of nine rational curves. The proof uses a correspondence between log Gromov-Witten invariants of the mirror and Vafa-Witten invariants of $\mathbb{P}^2$ established in previous work joint with Bousseau, together with known mock modularity results on the Vafa-Witten side. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08153 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mock modularity of log Gromov--Witten Invariants: the mirror to $\mathbb{P}^2$ Argüz, Hülya Algebraic Geometry High Energy Physics - Theory Symplectic Geometry We study modularity properties of generating series of logarithmic Gromov-Witten invariants of elliptic fibrations relative to singular fibers. Motivated by predictions from Vafa-Witten theory, we conjecture that such generating series are mock modular forms. We prove this conjecture for a large class of invariants of the rational elliptic surface mirror to $\mathbb{P}^2$, relative to a cycle of nine rational curves. The proof uses a correspondence between log Gromov-Witten invariants of the mirror and Vafa-Witten invariants of $\mathbb{P}^2$ established in previous work joint with Bousseau, together with known mock modularity results on the Vafa-Witten side. |
| title | Mock modularity of log Gromov--Witten Invariants: the mirror to $\mathbb{P}^2$ |
| topic | Algebraic Geometry High Energy Physics - Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2602.08153 |