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 talk, I will extend this correspondence by providing necessary and sufficient conditions for when a co-Higgs field induces an integrable 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. We will also analyze this correspondence for co-Higgs fields over curves of genus g greater than one. Finally, I will show how stability can be understood geometrically through the zeros of the induced Poisson structure, establishing connections between \Phi-invariant subbundles, Poisson subvarieties, and the spectral curve. As this talk is a preparation for my thesis defense, please ask me many questions!
MC 5403