Disk enumeration on the quintic 3-fold
Symplectic Geometry
2009-08-07 v2 High Energy Physics - Theory
Algebraic Geometry
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.
Cite
@article{arxiv.math/0610901,
title = {Disk enumeration on the quintic 3-fold},
author = {R. Pandharipande and J. Solomon and J. Walcher},
journal= {arXiv preprint arXiv:math/0610901},
year = {2009}
}
Comments
52 pages, 5 figures. Added background on open mirror symmetry in Section 0.4, and added details especially in Lemma 7 and Lemma 18