# Enumerative Geometry of Calabi-Yau 4-Folds

@article{Klemm2007EnumerativeGO, title={Enumerative Geometry of Calabi-Yau 4-Folds}, author={Albrecht Klemm and Rahul Pandharipande}, journal={Communications in Mathematical Physics}, year={2007}, volume={281}, pages={621-653} }

Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation.Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including the sextic Calabi-Yau in $${{\mathbb{P}^5…

## 94 Citations

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