From a hermitian metric on the anticanonical bundle on a Del Pezzo surface, and a holomorphic section of it, we construct a one-parameter family of bihermitian metrics (or equivalently generalized Kähler structures). The construction appears to be linked to noncommutative geometry.
Nigel Hitchin. "Bihermitian metrics on Del Pezzo surfaces." J. Symplectic Geom. 5 (1) 1 - 8, March 2007.