Scattering diagrams from holomorphic discs in log Calabi-Yau surfaces
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Lin, Yu-Shen
Bardwell-Evans, Sam A.
Cheung, Man-Wai
Hong, Hansol
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Y.-.S. Lin, S. Bardwell-Evans, M.-.W. Cheung, H. Hong. "Scattering diagrams from holomoprhic discs in log Calabi-Yau surfaces."
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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This version of the work is distributed under a Creative Commons Attribution 4.0 licence. Add to end of citation: https://arxiv.org/abs/2110.15234