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

Alessandro Chiodo[1]; Yongbin Ruan[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 (2011)

  • Volume: 61, Issue: 7, page 2803-2864
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Chiodo, Alessandro, and Ruan, Yongbin. "A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence." Annales de l’institut Fourier 61.7 (2011): 2803-2864. <http://eudml.org/doc/275578>.

@article{Chiodo2011,
abstract = {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.},
affiliation = {Institut de Mathématiques de Jussieu UMR 7586 CNRS Université Pierre et Marie Curie Case 247 4 Place Jussieu 75252 Paris cedex 05 France; Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA},
author = {Chiodo, Alessandro, Ruan, Yongbin},
journal = {Annales de l’institut Fourier},
keywords = {Mirror symmetry; Gromov–Witten theory; Calabi–Yau varieties; moduli of curves; mirror symmetry; Gromov-Witten theory; Calabi-Yau varieties},
language = {eng},
number = {7},
pages = {2803-2864},
publisher = {Association des Annales de l’institut Fourier},
title = {A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence},
url = {http://eudml.org/doc/275578},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Chiodo, Alessandro
AU - Ruan, Yongbin
TI - A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 7
SP - 2803
EP - 2864
AB - 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.
LA - eng
KW - Mirror symmetry; Gromov–Witten theory; Calabi–Yau varieties; moduli of curves; mirror symmetry; Gromov-Witten theory; Calabi-Yau varieties
UR - http://eudml.org/doc/275578
ER -

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