Differential Geometry Working Seminar

Brady Ali Medina, Department of Pure Mathematics, University of Waterloo

"Lifting a co-Higgs field to a Poisson structure"

A quadratic Poisson structure on a holomorphic vector bundle V with coisotropic fibers induces a co-Higgs field on V.  We could ask ourselves what does it take to recover the quadratic Poisson structure from its co-Higgs field.  It has been proven by Mykola M. that under certain conditions a co-Higgs field on a rank-2 vector bundle V over P^1 lifts to a Poisson structure on V. In this talk, we are going to show that it is possible to extend this result for a co-Higgs field on a rank-2 vector bundle V over a complex manifold. 

MC 5403