# $K_2$ and quantum curves

@inproceedings{Doran2021K\_2AQ, title={\$K\_2\$ and quantum curves}, author={Charles F. Doran and Matt Kerr and Soumya Sinha Babu}, year={2021} }

A 2015 conjecture of Codesido-Grassi-Mariño in topological string theory relates the enumerative invariants of toric CY 3-folds to the spectra of operators attached to their mirror curves. We deduce two consequences of this conjecture for the integral regulators of K2-classes on these curves, and then prove both of them; the results thus give evidence for the CGM conjecture. (While the conjecture and the deduction process both entail forms of local mirror symmetry, the consequences/theorems do…

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