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

  • Pierrick Bousseau (a1)

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 non-commutative algebras of functions.

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1

Current address: Institute for Theoretical Studies, ETH Zurich, 8092 Zurich, Switzerland email pboussea@ethz.ch

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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