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Journal of Noncommutative Geometry


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Volume 13, Issue 1, 2019, pp. 161–191
DOI: 10.4171/JNCG/314

Published online: 2018-12-17

Quantization of spectral curves and DQ-modules

François Petit[1]

(1) University of Luxembourg, Luxembourg

Given a holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, we prove the existence of a holonomic DQ-module supported by the spectral curve associated to this bundle. Then, we relate quantum curves arising in various situations (quantization of spectral curves of Higgs bundles, quantization of the $A$-polynomial…) to DQ-modules and show that a quantum curve and the DQ-module canonically associated to it have isomorphic sheaves of solutions.

Keywords: DQ-module, quantum curves, spectral curves, deformation quantization, Higgs bundle

Petit François: Quantization of spectral curves and DQ-modules. J. Noncommut. Geom. 13 (2019), 161-191. doi: 10.4171/JNCG/314