Stable Pair Invariants of Local Calabi–Yau 4-folds

  title={Stable Pair Invariants of Local Calabi–Yau 4-folds},
  author={Yalong Cao and Martijn Kool and Sergej Monavari},
  journal={International Mathematics Research Notices},
In 2008, Klemm–Pandharipande defined Gopakumar–Vafa type invariants of a Calabi–Yau 4-folds $X$ using Gromov–Witten theory. Recently, Cao–Maulik–Toda proposed a conjectural description of these invariants in terms of stable pair theory. When $X$ is the total space of the sum of two line bundles over a surface $S$, and all stable pairs are scheme theoretically supported on the zero section, we express stable pair invariants in terms of intersection numbers on Hilbert schemes of points on $S… 
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