Quantum mirrors of log CalabiYau surfaces and higher genus curve counting
Abstract
Gross, Hacking, and Keel have constructed mirrors of log CalabiYau surfaces in terms of counts of rational curves. Using $q$deformed scattering diagrams defined in terms of higher genus log GromovWitten invariants, we construct deformation quantizations of these mirrors and we produce canonical bases of the corresponding noncommutative algebras of functions.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.07336
 Bibcode:
 2018arXiv180807336B
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra;
 Mathematics  Symplectic Geometry
 EPrint:
 v2: 55 pages, revised version, published in Compositio Math