Generalized B-Opers

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dc.contributor.authorBiswas, Indranil
dc.contributor.authorSchaposnik, Laura P.
dc.contributor.authorYang, Mengxue
dc.date.accessioned2025-12-15T15:26:39Z
dc.date.issued2020
dc.description.abstractOpers 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.
dc.description.sponsorshipThe 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.
dc.identifier.citationGeneralized B-Opers. Indranil Biswas, Laura P. Schaposnik and Mengxue Yang. SIGMA 16 (2020), 041, 28 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.041
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 14H60; 31A35; 33C80; 53C07
dc.identifier.otherarXiv:1911.11842
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210709
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleGeneralized B-Opers
dc.typeArticle

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