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

  • Pierrick Bousseau (a1)


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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Current address: Institute for Theoretical Studies, ETH Zurich, 8092 Zurich, Switzerland email

This work is supported by EPSRC award 1513338, ‘Counting curves in algebraic geometry’, Imperial College London, and has benefited from the EPRSC [EP/L015234/1], EPSRC Centre for Doctoral Training in Geometry and Number Theory (London School of Geometry and Number Theory), University College London.



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

  • Pierrick Bousseau (a1)


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