Interplay between Opers, Quantum Curves, WKB Analysis, and Higgs Bundles

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Dumitrescu, Olivia, Mulase, Motohico
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211313
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Interplay between Opers, Quantum Curves, WKB Analysis, and Higgs Bundles. Olivia Dumitrescu and Motohico Mulase. SIGMA 17 (2021), 036, 53 pages

Quantum curves were introduced in the physics literature. We develop a mathematical framework for the case associated with Hitchin spectral curves. In this context, a quantum curve is a Rees 𝒟-module on a smooth projective algebraic curve, whose semi-classical limit produces the Hitchin spectral cur...