As an analogy to the Gopakumar–Vafa conjecture on CY 3-folds, Klemm–Pandharipande defined GV type invariants on CY 4-folds using GW theory and conjectured their integrality. In this paper, we define stable pair type invariants on CY 4-folds and use them to interpret these GV type invariants. Examples are computed for both compact and non-compact CY 4-folds to support our conjectures.
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Yalong Cao, Davesh Maulik, Yukinobu Toda, Stable pairs and Gopakumar–Vafa type invariants for Calabi–Yau 4-folds. J. Eur. Math. Soc. 24 (2022), no. 2, pp. 527–581DOI 10.4171/JEMS/1110