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A proof of the Landau-Ginzburg/Calabi-Yau correspondence via the crepant transformation conjecture

Nathan Priddis Institut für Algebraische Geometrie, Universität Hannover, D-30060 Hannover Yuan-Pin Lee Department of Mathematics, University of Utah, Salt Lake City, UT 84112 Mark Shoemaker Department of Mathematics, Colorado State University Fort Collins, CO 80523

Algebraic Geometry mathscidoc:2204.45008

2014.10
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.
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@inproceedings{nathan2014a,
  title={A proof of the Landau-Ginzburg/Calabi-Yau correspondence via the crepant transformation conjecture},
  author={Nathan Priddis, Yuan-Pin Lee, and Mark Shoemaker},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415111028605401026},
  year={2014},
}
Nathan Priddis, Yuan-Pin Lee, and Mark Shoemaker. A proof of the Landau-Ginzburg/Calabi-Yau correspondence via the crepant transformation conjecture. 2014. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415111028605401026.
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