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Open Gromov–Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing

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In this paper, we study holomorphic discs in K3 surfaces and defined the open Gromov–Witten invariants. Using this new invariant, we can establish a version of correspondence between tropical discs and holomorphic discs with non-trivial invariants. We give an example of wall-crossing phenomenon of the invariant and expect it satisfies Kontsevich–Soibelman wall-crossing formula.

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Correspondence to Yu-Shen Lin.

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Communicated by H.-T. Yau

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Lin, YS. Open Gromov–Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing. Commun. Math. Phys. 349, 109–164 (2017).

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