Enumerative Geometry of Calabi-Yau 4-Folds |
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Authors: | A Klemm R Pandharipande |
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Institution: | (1) Department of Physics, Univ. of Wisconsin, Madison, WI 53706, USA;(2) Department of Mathematics, Princeton University, Princeton, NJ 08544, USA |
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Abstract: | 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 , are also studied. A complete solution of the Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic
anomaly equation. |
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Keywords: | |
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