Triply Periodic Monopoles and Difference Modules on Elliptic Curves

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dc.contributor.authorMochizuki, Takuro
dc.date.accessioned2025-12-15T15:24:52Z
dc.date.issued2020
dc.description.abstractWe explain the correspondences between twisted monopoles with Dirac-type singularity and polystable twisted mini-holomorphic bundles with Dirac-type singularity on a 3-dimensional torus. We also explain that they are equivalent to polystable parabolic twisted difference modules on elliptic curves.
dc.description.sponsorshipI thank Maxim Kontsevich and Yan Soibelman for the communications and for sending the preprint [2]. Indeed, this study grew out of my answer to one of their questions. They also kindly suggested that there should be a generalization to the twisted case. I hope that this will be useful for their big project. I owe much to Carlos Simpson, whose ideas on the Kobayashi-Hitchin correspondence are fundamental in this study. I thank Masaki Yoshino for the discussions. I thank the referees for their careful readings and valuable comments. I am grateful to the organizers of the conference Integrability, Geometry and Moduli to celebrate the 60th birthday of Motohico Mulase. The twisted version of the equivalences was explained in my talk at the conference. It is my great pleasure to dedicate this paper to Motohico Mulase with appreciation for his friendly encouragement and suggestions on many occasions. I am partially supported by the Grant-in-Aid for Scientific Research (S) (No. 17H06127), the Grant-in-Aid for Scientific Research (S) (No. 16H06335), the Grant-in-Aid for Scientific Research (C) (No. 15K04843), the Grant-in-Aid for Scientific Research (C) (No. 20K03609), Japan Society for the Promotion of Science.
dc.identifier.citationTriply Periodic Monopoles and Difference Modules on Elliptic Curves. Takuro Mochizuki. SIGMA 16 (2020), 048, 23 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.048
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 53C07; 58E15; 14D21; 81T13
dc.identifier.otherarXiv:1903.03264
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210702
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleTriply Periodic Monopoles and Difference Modules on Elliptic Curves
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік