
SIGMA 16 (2020), 048, 23 pages arXiv:1903.03264
https://doi.org/10.3842/SIGMA.2020.048
Contribution to the Special Issue on Integrability, Geometry, Moduli in honor of Motohico Mulase for his 65th birthday
Triply Periodic Monopoles and Difference Modules on Elliptic Curves
Takuro Mochizuki
Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 6068502, Japan
Received October 29, 2019, in final form May 18, 2020; Published online June 03, 2020
Abstract
We explain the correspondences between twisted monopoles with Dirac type singularity and polystable twisted miniholomorphic bundles with Dirac type singularity on a 3dimensional torus. We also explain that they are equivalent to polystable parabolic twisted difference modules on elliptic curves.
Key words: twisted monopoles; twisted difference modules; twisted miniholomorphic bundles; KobayashiHitchin correspondence.
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References
 Charbonneau B., Hurtubise J., Singular HermitianEinstein monopoles on the product of a circle and a Riemann surface, Int. Math. Res. Not. 2011 (2011), 175216, arXiv:0812.0221.
 Kontsevich M., Soibelman Y., RiemannHilbert correspondence in dimension one, Fukaya categories and periodic monopoles, Preprint.
 Kronheimer P.B., Monopoles and TaubNUT metrics, Master Thesis, Oxford, 1986.
 Mochizuki T., Periodic monopoles and difference modules, arXiv:1712.08981.
 Mochizuki T., Doublyperiodic monopoles and $q$difference modules, arXiv:1902.08298.
 Mochizuki T., Yoshino M., Some characterizations of Dirac type singularity of monopoles, Comm. Math. Phys. 356 (2017), 613625, arXiv:1702.06268.
 Simpson C.T., Constructing variations of Hodge structure using YangMills theory and applications to uniformization, J. Amer. Math. Soc. 1 (1988), 867918.
 Yoshino M., A KobayashiHitchin correspondence between Diractype singular miniholomorphic bundles and HEmonopoles, arXiv:1902.09995.

