Triply Periodic Monopoles and Difference Modules on Elliptic Curves
We 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.
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210702 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Triply Periodic Monopoles and Difference Modules on Elliptic Curves. Takuro Mochizuki. SIGMA 16 (2020), 048, 23 pages |
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Mochizuki, Takuro 2025-12-15T15:24:52Z 2020 Triply Periodic Monopoles and Difference Modules on Elliptic Curves. Takuro Mochizuki. SIGMA 16 (2020), 048, 23 pages 1815-0659 2020 Mathematics Subject Classification: 53C07; 58E15; 14D21; 81T13 arXiv:1903.03264 https://nasplib.isofts.kiev.ua/handle/123456789/210702 https://doi.org/10.3842/SIGMA.2020.048 We 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. I 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Triply Periodic Monopoles and Difference Modules on Elliptic Curves Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Triply Periodic Monopoles and Difference Modules on Elliptic Curves |
| spellingShingle |
Triply Periodic Monopoles and Difference Modules on Elliptic Curves Mochizuki, Takuro |
| title_short |
Triply Periodic Monopoles and Difference Modules on Elliptic Curves |
| title_full |
Triply Periodic Monopoles and Difference Modules on Elliptic Curves |
| title_fullStr |
Triply Periodic Monopoles and Difference Modules on Elliptic Curves |
| title_full_unstemmed |
Triply Periodic Monopoles and Difference Modules on Elliptic Curves |
| title_sort |
triply periodic monopoles and difference modules on elliptic curves |
| author |
Mochizuki, Takuro |
| author_facet |
Mochizuki, Takuro |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We 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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210702 |
| citation_txt |
Triply Periodic Monopoles and Difference Modules on Elliptic Curves. Takuro Mochizuki. SIGMA 16 (2020), 048, 23 pages |
| work_keys_str_mv |
AT mochizukitakuro triplyperiodicmonopolesanddifferencemodulesonellipticcurves |
| first_indexed |
2025-12-17T12:04:31Z |
| last_indexed |
2025-12-17T12:04:31Z |
| _version_ |
1851756979355123712 |