PhD Thesis Defense
Brady Ali Medina, University of Waterloo
Co-Higgs Bundles and Poisson Structures.
There is a correspondence between co-Higgs fields and holomorphic Poisson structures on P(V) established by Polishchuk in the rank 2 case and by Matviichuk in the case where the co-Higgs field is diagonalizable. In this thesis, we extend this correspondence by providing necessary and sufficient conditions for when a co-Higgs field induces a Poisson structure on V and P(V), showing that the co-Higgs field must either be a function multiple of a constant matrix or have only one non-zero column. Furthermore, we analyze this correspondence for co-Higgs fields over curves of genus greater or equal to one. Finally, we analyze how stability can be interpreted geometrically through the zeros of the induced Poisson structure, establishing connections between \Phi -invariant subbundles, Poisson subvarieties, and the spectral curve.
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Meeting ID: 971 4907 1044
Passcode: 776121