Generalized B-Opers
Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42], a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We dedicate this paper to introducing and studying generalized B...
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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: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210709 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Generalized B-Opers. Indranil Biswas, Laura P. Schaposnik and Mengxue Yang. SIGMA 16 (2020), 041, 28 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862744341056847872 |
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| author | Biswas, Indranil Schaposnik, Laura P. Yang, Mengxue |
| author_facet | Biswas, Indranil Schaposnik, Laura P. Yang, Mengxue |
| citation_txt | Generalized B-Opers. Indranil Biswas, Laura P. Schaposnik and Mengxue Yang. SIGMA 16 (2020), 041, 28 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42], a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We dedicate this paper to introducing and studying generalized B-opers (where ''B'' stands for ''bilinear''), obtained by endowing the underlying vector bundle with a bilinear form which is compatible with both the filtration and the connection. In particular, we study the structure of these B-opers by considering the relationship of these structures with jet bundles and with geometric structures on a Riemann surface.
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| first_indexed | 2025-12-17T12:04:33Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210709 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:33Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Biswas, Indranil Schaposnik, Laura P. Yang, Mengxue 2025-12-15T15:26:39Z 2020 Generalized B-Opers. Indranil Biswas, Laura P. Schaposnik and Mengxue Yang. SIGMA 16 (2020), 041, 28 pages 1815-0659 2020 Mathematics Subject Classification: 14H60; 31A35; 33C80; 53C07 arXiv:1911.11842 https://nasplib.isofts.kiev.ua/handle/123456789/210709 https://doi.org/10.3842/SIGMA.2020.041 Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42], a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We dedicate this paper to introducing and studying generalized B-opers (where ''B'' stands for ''bilinear''), obtained by endowing the underlying vector bundle with a bilinear form which is compatible with both the filtration and the connection. In particular, we study the structure of these B-opers by considering the relationship of these structures with jet bundles and with geometric structures on a Riemann surface. The authors are grateful for the hospitality and support of the Simons Center for Geometry and Physics program Geometry & Physics of Hitchin Systems, co-organized by L. Anderson and L.P. Schaposnik, where this project started. In particular, they would like to thank Andy Sanders for his seminar at the program [31], which inspired some of the ideas in this paper. Finally, we would like to thank Brian Collier, Aaron Fenyes, Nigel Hitchin, Steve Rayan, and Sebastian Schulz for comments on a draft of the manuscript. The authors are also thankful for all the very useful comments from the two anonymous referees, whose suggestions greatly improved the manuscript. LS is grateful for Motohico Mulase's support and encouragement over the years. She is partially supported by the NSF grant DMS-1509693, the NSF CAREER Award DMS-1749013, and by the Alexander von Humboldt Foundation. This material is also based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2019 semester. IB is supported by a J.C. Bose Fellowship. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Generalized B-Opers Article published earlier |
| spellingShingle | Generalized B-Opers Biswas, Indranil Schaposnik, Laura P. Yang, Mengxue |
| title | Generalized B-Opers |
| title_full | Generalized B-Opers |
| title_fullStr | Generalized B-Opers |
| title_full_unstemmed | Generalized B-Opers |
| title_short | Generalized B-Opers |
| title_sort | generalized b-opers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210709 |
| work_keys_str_mv | AT biswasindranil generalizedbopers AT schaposniklaurap generalizedbopers AT yangmengxue generalizedbopers |