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Disk enumeration on the quintic 3-fold
Author(s):
R.
Pandharipande;
J.
Solomon;
J.
Walcher
Journal:
J. Amer. Math. Soc.
21
(2008),
1169-1209.
MSC (2000):
Primary 53D45, 14N35;
Secondary 14J32
Posted:
February 12, 2008
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Additional information
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:
10.1090/S0894-0347-08-00597-3
PII:
S 0894-0347(08)00597-3
Received by editor(s):
May 29, 2007
Posted:
February 12, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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