A comparison of deformations and geometric study of varieties of associative algebras.
Additive deformations of bialgebras in the sense of J. Wirth [PhD thesis, Université Paris VI, 2002], i.e. deformations of the multiplication map fulfilling a certain compatibility condition with respect to the coalgebra structure, can be generalized to braided bialgebras. The theorems for additive deformations of Hopf algebras can also be carried over to that case. We consider *-structures and prove a general Schoenberg correspondence in this context. Finally we give some examples.