Generalized Opers

In this thesis we collect the results from three papers: “Generalized B-opers”, “On the generalized SO(2n,C)-opers”, and “A comparison of generalized opers and (G,P)-opers”. We first give an expository introduction on classical G-opers, complex projective structures and Higgs bundles to motivate our study of generalized opers. We then introduce generalized B-opers and show that they can be parametrized by a flat orthogonal bundle and a classical oper. We give an example of generalized B-opers on jet bundles, and an example of a stable Higgs bundle arising from a generalized B-oper. Then we introduce the generalized SO(2n,C)-oper which do not arise as naturally as the generalized B-opers and describe their parameter space. Finally we draw an explicit comparison between generalized B-opers and (G,P)-opers, which are a more relaxed generalization of G-opers.