On the generalized SO(2n,C)-opers
Abstract
Since their introduction by Beilinson-Drinfeld BD,Opers1, opers have seen several generalizations. In BSY a higher rank analog was studied, named generalized B-opers, where the successive quotients of the oper filtration are allowed to have higher rank and the underlying holomorphic vector bundle is endowed with a bilinear form which is compatible with both the filtration and the oper connection. Since the definition didn't encompass the even orthogonal groups, we dedicate this paper to study generalized B-opers whose structure group is SO(2n,C), and show their close relationship with geometric structures on a Riemann surface.
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