A new method toward the Landau–Ginzburg/Calabi–Yau correspondence via quasi-maps

  • Jinwon ChoiEmail author
  • Young-Hoon Kiem


The Landau–Ginzburg/Calabi–Yau correspondence claims that the Gromov–Witten invariant of the quintic Calabi–Yau 3-fold should be related to the Fan–Jarvis–Ruan–Witten invariant of the associated Landau–Ginzburg model via wall crossings. In this paper, we consider the stack of quasi-maps with a cosection and introduce sequences of stability conditions which enable us to interpolate between the moduli stack for Gromov–Witten invariants and the moduli stack for Fan–Jarvis–Ruan–Witten invariants.

Mathematics Subject Classification

14D23 14N35 



We thank Huai-Liang Chang, Emily Clader, Tyler Jarvis, Bumsig Kim, Jun Li and Yongbin Ruan for useful discussions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Research Institute of Natural SciencesSookmyung Women’s UniversitySeoulSouth Korea
  2. 2.Department of Mathematics and Research Institute of MathematicsSeoul National UniversitySeoulSouth Korea

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