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.
- Pub Date:
- August 2018
- Mathematics - Algebraic Geometry;
- High Energy Physics - Theory;
- Mathematics - Quantum Algebra;
- Mathematics - Symplectic Geometry
- v2: 55 pages, revised version, published in Compositio Math