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Annales scientifiques de l'ENS - Parutions - série 4, 49 (2016)

Parutions < série 4, 49

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 49, fascicule 6 (2016)

Yuan-Pin Lee, Nathan Priddis, Mark Shoemaker
A proof of the Landau-Ginzburg/Yau correspondence via the crepant transformation conjecture
Annales scientifiques de l'ENS 49, fascicule 6 (2016), 1403-1443

Télécharger cet article : Fichier PDF

Résumé :
Une preuve de la correspondance de Landau-Ginzburg/Calabi-Yau via la conjecture de la transformation crépante
Nous établissons une nouvelle relation (la correspondance MLK) entre la théorie FJRW twistée et la théorie de Gromov-Witten en tout genre. Cela nous permet de montrer que la conjecture de la transformation crépante pour le type de Fermat en genre zéro implique la correspondance de Landau-Ginzburg/Calabi-Yau. Nous nous servons de ce résultat pour prouver la correspondance de Landau-Ginzburg/Calabi-Yau pour le type de Fermat, généralisant les résultats de A. Chiodo et Y. Ruan de [20].

Mots-clefs : Résolution crépante, correspondance de Landau-Ginzburg/Calabi-Yau, symétrie miroir, correspondance MLK.

Abstract:
We establish a new relationship (the MLK correspondence) between twisted FJRW theory and local Gromov-Witten theory in all genera. As a consequence, we show that the Landau-Ginzburg/Calabi-Yau correspondence is implied by the crepant transformation conjecture for Fermat type in genus zero. We use this to then prove the Landau-Ginzburg/Calabi-Yau correspondence for Fermat type, generalizing the results of A. Chiodo and Y. Ruan in [20].

Keywords: Crepant resolution, Landau-Ginzburg/Calabi-Yau correspondence, mirror symmetry, MLK correspondence.

Class. math. : 14N35, 14A20, 14E16, 53D45


ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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