Geodesic
Disk enumeration on the quintic 3-fold
Pandharipande, R.1 ; Solomon, J.2, 1 ; Walcher, J.3
1 Department of Mathematics, Princeton University, Princeton, New Jersey 08544
2 School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
3 School of Natural Science, Institute for Advanced Study, Princeton, New Jersey 08540
Journal of the American Mathematical Society, Tome 21 (2008) no. 4, pp. 1169-1209

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-08-00597-3

Pandharipande, R. 1 ; Solomon, J. 2, 1 ; Walcher, J. 3

1 Department of Mathematics, Princeton University, Princeton, New Jersey 08544
2 School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
3 School of Natural Science, Institute for Advanced Study, Princeton, New Jersey 08540 
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Pandharipande, R.; Solomon, J.; Walcher, J. Disk enumeration on the quintic 3-fold. Journal of the American Mathematical Society, Tome 21 (2008) no. 4, pp. 1169-1209. doi: 10.1090/S0894-0347-08-00597-3

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