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

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics and Research Institute of Natural Sciences, Sookmyung Women’s University, Seoul, 04310, South Korea

    **won Choi

  2. Department of Mathematics and Research Institute of Mathematics, Seoul National University, Seoul, 08826, South Korea

    Young-Hoon Kiem

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  1. **won Choi
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  2. Young-Hoon Kiem
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Correspondence to **won Choi.

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**won Choi was supported by NRF Grants NRF-2015R1C1A1A01054185 and NRF-2018R1C1B6005600. Young-Hoon Kiem was partially supported by Samsung Science and Technology Foundation Grant SSTF-BA1601-01.

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Choi, J., Kiem, YH. A new method toward the Landau–Ginzburg/Calabi–Yau correspondence via quasi-maps. Math. Z. 294, 161–199 (2020). https://doi.org/10.1007/s00209-019-02249-1

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