# Stable Pair Invariants of Local Calabi–Yau 4-folds

@article{Cao2020StablePI, title={Stable Pair Invariants of Local Calabi–Yau 4-folds}, author={Yalong Cao and Martijn Kool and Sergej Monavari}, journal={International Mathematics Research Notices}, year={2020} }

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…

## 15 Citations

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