Disk enumeration on the quintic 3-fold

Details Disk enumeration on the quintic 3-fold Disk enumeration on the quintic 3-fold

2006-10-29

arxiv.org/abs/math/0610901v2

J. Amer. Math. Soc. 21 (2008), 1169-1209.

Mathematics

Symplectic Geometry

52 pages, 5 figures. Added background on open mirror symmetry in Section 0.4, and added details especially in Lemma 7 and Lemm

Scientific paper

10.1090/S0894-0347-08-00597-3

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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