Holomorphic versus algebraic equivalence for deformations of   real-algebraic CR manifolds
  We consider (small) algebraic deformations of germs of real-algebraic CR submanifolds in complex space and study the biholomorphic equivalence problem for such deformations. We show that two algebraic deformations of minimal holomorphically nondegenerate real-algebraic CR submanifolds are holomorphically equivalent if and only if they are algebraically equivalent. 
Bernhard Lamel and Nordine Mir
math.CV math.AG