Goto’s generalized Kähler stability theorem

In these notes we give a shortened and more direct proof of Goto’s generalized Kähler stability theorem stating that if (J1,J2)(J1,J2) is a generalized Kähler structure for which J2J2 is determined by a nowhere vanishing closed form, then small deformations of J1J1 can be coupled with small deformations of J2J2 so that the pair remains a generalized Kähler structure.