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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 041, 28 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.041 (Mi sigma1578) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Generalized B-Opers

Indranil Biswasa, Laura P. Schaposnikb, Mengxue Yangb

a Tata Institute of Fundamental Research, India
b University of Illinois at Chicago, USA
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DOI: https://doi.org/10.3842/SIGMA.2020.041
Abstract: 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.
Keywords: opers, connection, projective structure, Higgs bundles, differential operator, Lagrangians.
Funding agency Grant number
Simons Center for Geometry and Physics
National Science Foundation DMS-1509693
DMS-1749013
DMS-1440140
Alexander von Humboldt-Stiftung
Science and Engineering Research Board J.C. Bose Fellowship
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. 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.
Received: November 28, 2019; in final form May 2, 2020; Published online May 14, 2020
Bibliographic databases:
Document Type: Article
MSC: 14H60, 31A35, 33C80, 53C07
Language: English
Citation: Indranil Biswas, Laura P. Schaposnik, Mengxue Yang, “Generalized B-Opers”, SIGMA, 16 (2020), 041, 28 pp.
Citation in format AMSBIB
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\paper Generalized B-Opers
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\vol 16
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    		Symmetry, Integrability and Geometry: Methods and Applications
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