Quantum mirrors of log Calabi–Yau surfaces and higher-genus curve counting

  title={Quantum mirrors of log Calabi–Yau surfaces and higher-genus curve counting},
  author={Pierrick Bousseau},
  journal={Compositio Mathematica},
  pages={360 - 411}
Gross, Hacking and Keel have constructed mirrors of log Calabi–Yau surfaces in terms of counts of rational curves. Using $q$-deformed scattering diagrams defined in terms of higher-genus log Gromov–Witten invariants, we construct deformation quantizations of these mirrors and we produce canonical bases of the corresponding non-commutative algebras of functions. 

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