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Disk enumeration on the quintic 3-fold

R. Pandharipande·J. Solomon·J. Walcher
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Abstract

Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for the disk invariants is shown to satisfy an extension of the Picard-Fuchs differential equations associated to the mirror quintic. The Ooguri-Vafa multiple cover formula is used to define virtually enumerative disk invariants. The results may also be viewed as providing a virtual enumeration of real rational curves on the quintic.

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R. Pandharipande, J. Solomon, J. Walcher. 2007-05-28. Disk enumeration on the quintic 3-fold. https://doi.org/10.1090/s0894-0347-08-00597-3

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