Generalized holomorphic bundles and the B-field action

On a generalized complex manifold, there is an associated definition of a generalized holomorphic bundle, introduced by Gualtieri. In the case of an ordinary complex structure, this notion yields an object which we call a co-Higgs bundle, and we consider the B-field action of a closed form of type (1,1)$(1,1)$, both local and global. The effect makes contact with both Nahm’s equations and holomorphic gerbes.