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arXiv · 2602.08153

Mock modularity of log Gromov--Witten Invariants: the mirror to $\mathbb{P}^2$

Hülya Argüz
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Abstract

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.

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Hülya Argüz. 2026-02-08. Mock modularity of log Gromov--Witten Invariants: the mirror to $\mathbb{P}^2$. https://arxiv.org/abs/2602.08153

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