A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence

Chiodo, Alessandro; Ruan, Yongbin

A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence
[Un cadre de symétrie miroir globale pour la correspondance Landau–Ginzburg/Calabi–Yau]

Chiodo, Alessandro ; Ruan, Yongbin

Annales de l'Institut Fourier, Tome 61 (2011), p. 2803-2864 / Harvested from Numdam

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Résumé
Abstract

On montre comment la correspondance Landau–Ginzburg/Calabi–Yau pour la variété quintique dans $ℙ^{4}$ s’inscrit naturellement dans un cadre de symétrie miroir globale. On s’inspire de la dualité miroir de Berglund–Hübsch pour fournir un cadre conjectural analogue qui incorpore toutes les hypersurfaces de Calabi–Yau dans les espaces projectifs à poids, ainsi que certains quotients par l’action de groupes abéliens finis.

We show how the Landau–Ginzburg/Calabi–Yau correspondence for the quintic three-fold can be cast into a global mirror symmetry framework. Then we draw inspiration from Berglund–Hübsch mirror duality construction to provide an analogue conjectural picture featuring all Calabi–Yau hypersurfaces within weighted projective spaces and certain quotients by finite abelian group actions.

Publié le : 2011-01-01

MR 3112509 | Zbl pre06193028

DOI : https://doi.org/10.5802/aif.2795
Classification: 14J33, 14J32, 14H10
Mots clés: Symétrie miroir, théorie de Gromov–Witten, variétés de Calabi–Yau, modules de courbes

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     author = {Chiodo, Alessandro and Ruan, Yongbin},
     title = {A global mirror symmetry framework for the Landau--Ginzburg/Calabi--Yau correspondence},
     journal = {Annales de l'Institut Fourier},
     volume = {61},
     year = {2011},
     pages = {2803-2864},
     doi = {10.5802/aif.2795},
     zbl = {pre06193028},
     mrnumber = {3112509},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2011__61_7_2803_0}
}

Chiodo, Alessandro; Ruan, Yongbin. A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence. Annales de l'Institut Fourier, Tome 61 (2011) pp. 2803-2864. doi : 10.5802/aif.2795. http://gdmltest.u-ga.fr/item/AIF_2011__61_7_2803_0/

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