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arXiv · 1808.07336

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

Pierrick Bousseau
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Abstract

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 noncommutative algebras of functions.

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Pierrick Bousseau. 2018-08-22. Quantum mirrors of log Calabi-Yau surfaces and higher genus curve counting. https://doi.org/10.1112/s0010437x19007760

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