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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Disk enumeration on the quintic 3-fold


Authors: R. Pandharipande, J. Solomon and J. Walcher
Journal: J. Amer. Math. Soc. 21 (2008), 1169-1209
MSC (2000): Primary 53D45, 14N35; Secondary 14J32
Published electronically: February 12, 2008
MathSciNet review: 2425184
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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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Additional Information

R. Pandharipande
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
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
Email: walcher@ias.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-08-00597-3
PII: S 0894-0347(08)00597-3
Received by editor(s): May 29, 2007
Published electronically: February 12, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.