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… 
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94 Citations
Highly Influential Citations
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Background Citations
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Methods Citations
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Results Citations
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94 Citations

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