  It is shown that a formal mapping between two real-analytic hypersurfaces in
complex space is convergent provided that neither hypersurface contains a
nontrivial holomorphic variety. For higher codimensional generic submanifolds,
convergence is proved e.g. under the assumption that the source is of finite
type, the target does not contain a nontrivial holomorphic variety, and the
mapping is finite. Finite determination (by jets of a predetermined order) of
formal mappings between smooth generic submanifolds is also established.
