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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

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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.
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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