JournalsjncgVol. 13, No. 1pp. 161–191

Quantization of spectral curves and DQ-modules

  • François Petit

    University of Luxembourg, Luxembourg
Quantization of spectral curves and DQ-modules cover

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Abstract

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 AA-polynomial…) to DQ-modules and show that a quantum curve and the DQ-module canonically associated to it have isomorphic sheaves of solutions.

Cite this article

François Petit, Quantization of spectral curves and DQ-modules. J. Noncommut. Geom. 13 (2018), no. 1, pp. 161–191

DOI 10.4171/JNCG/314