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arXiv · 2110.15234

Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces

Sam Bardwell-Evans·Man-Wai Mandy Cheung·Hansol Hong·Yu-Shen Lin
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Abstract

We construct special Lagrangian fibrations for log Calabi-Yau surfaces, and scattering diagrams from Lagrangian Floer theory of the fibres. Then we prove that the scattering diagrams recover the scattering diagrams of Gross-Pandharipande-Siebert and the canonical scattering diagrams of Gross-Hacking-Keel. With an additional assumption on the non-negativity of boundary divisors, we compute the disc potentials of the Lagrangian torus fibres via a holomorphic/tropical correspondence. As an application, we provide a version of mirror symmetry for rank two cluster varieties.

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Sam Bardwell-Evans, Man-Wai Mandy Cheung, Hansol Hong, Yu-Shen Lin. 2021-10-28. Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces. https://arxiv.org/abs/2110.15234

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