## On the tropical discs counting on elliptic K3 surfaces with general singular fibres

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## Abstract:

Using Lagrangian Floer theory, we study the tropical geometry of K3 surfaces with more general singular fibres other than simple nodal curves. In particular, we give the local models for the types $I_n$, $II$, $III$ and $IV$ singular fibres in the Kodaira classification. This generalizes the correspondence theorem in “Correspondence theorem between holomorphic discs and tropical discs on K3 surfaces”, arXiv:1703.00411 between open Gromov-Witten invariants/tropical discs counting to these cases.## References

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## Additional Information

**Yu-Shen Lin**- Affiliation: Center of Mathematical Sciences and Applications, 20 Garden Street, Cambridge, Massachusetts 02139
- Address at time of publication: Boston University, 111 Cummington Mall, Boston, Massachusetts 02215
- MR Author ID: 1192962
- Email: yslin@bu.edu
- Received by editor(s): April 8, 2018
- Received by editor(s) in revised form: August 7, 2019
- Published electronically: November 1, 2019
- Additional Notes: The author was supported by the Center of Mathematical Sciences and Applications at Harvard University at the time of submitting the paper.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**373**(2020), 1385-1405 - MSC (2010): Primary 14N10, 37J05
- DOI: https://doi.org/10.1090/tran/7961
- MathSciNet review: 4068267