BPS invariants of symplectic log Calabi-Yau fourfolds (Q6567169)

The main result of this paper is a proof of a conjecture of \textit{M. Gross} et al. [Duke Math. J. 153, No. 2, 297--362 (2010; Zbl 1205.14069)] on the BPS integrality of genus \(0\) 1-pointed log Gromov-Witten invariants of log Calabi-Yau surfaces. This result is proved using symplectic techniques. Remarkably, the author shows that for generic choice of compatible almost Kähler structures, the relevant moduli spaces of maps decomposes into smooth orbifold connected components parametrizing multiple covers of finitely many generically injective curves, with explicit obstruction bundles. The author also obtains partial result towards a higher-genus version of the BPS integrality conjecture formulated by \textit{P. Bousseau} [Geom. Topol. 24, No. 3, 1297--1379 (2020; Zbl 1451.14158)], and proposes a refined conjecture in the genus one case.