## Disk enumeration on the quintic 3-fold

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- by R. Pandharipande, J. Solomon and J. Walcher
- J. Amer. Math. Soc.
**21**(2008), 1169-1209 - DOI: https://doi.org/10.1090/S0894-0347-08-00597-3
- Published electronically: February 12, 2008
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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.## References

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## Bibliographic Information

**R. Pandharipande**- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- MR Author ID: 357813
- Email: rahulp@math.princeton.edu
**J. Solomon**- Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
- Address at time of publication: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- Email: jake@ias.edu, jake@math.princeton.edu
**J. Walcher**- Affiliation: School of Natural Science, Institute for Advanced Study, Princeton, New Jersey 08540
- MR Author ID: 656979
- Email: walcher@ias.edu
- Received by editor(s): May 29, 2007
- Published electronically: February 12, 2008
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**21**(2008), 1169-1209 - MSC (2000): Primary 53D45, 14N35; Secondary 14J32
- DOI: https://doi.org/10.1090/S0894-0347-08-00597-3
- MathSciNet review: 2425184