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

Lin, Yu-Shen

doi:10.1090/tran/7961

On the tropical discs counting on elliptic K3 surfaces with general singular fibres
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Trans. Amer. Math. Soc. 373 (2020), 1385-1405 Request permission

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.

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