On the generalized SO(2n,C)-opers

Abstract

Since their introduction by Beilinson-Drinfeld \cite{BD,Opers1}, opers have seen several generalizations. In \cite{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 $\mathrm{SO}(2n,\mathbb{C})$, and show their close relationship with geometric structures on a Riemann surface.

Final version; to appear in "Annals of Global Analysis and Geometry"

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• Generalized B-Opers