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

Chiodo, Alessandro; Ruan, Yongbin

doi:10.5802/aif.2795

Chiodo, Alessandro ¹; Ruan, Yongbin ²

¹ Institut de Mathématiques de Jussieu UMR 7586 CNRS Université Pierre et Marie Curie Case 247 4 Place Jussieu 75252 Paris cedex 05 France
² Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA

Annales de l'Institut Fourier, Volume 61 (2011) no. 7, pp. 2803-2864.

Abstract
Résumé

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.

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.

MR: 3112509

DOI: 10.5802/aif.2795

Classification: 14J33, 14J32, 14H10
Keywords: Mirror symmetry, Gromov–Witten theory, Calabi–Yau varieties, moduli of curves
Mot clés : Symétrie miroir, théorie de Gromov–Witten, variétés de Calabi–Yau, modules de courbes

Author's affiliations:

Chiodo, Alessandro ¹; Ruan, Yongbin ²

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     journal = {Annales de l'Institut Fourier},
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     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Chiodo, Alessandro; Ruan, Yongbin. A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence. Annales de l'Institut Fourier, Volume 61 (2011) no. 7, pp. 2803-2864. doi : 10.5802/aif.2795. https://aif.centre-mersenne.org/articles/10.5802/aif.2795/

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