Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds

Abstract

As an analogy to 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.

35 pages, exposition improved, to appear in J. Eur. Math. Soc. (JEMS). arXiv admin note: text overlap with arXiv:1801.02513

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