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Let  D ( n, s, k ) = { z ∈ ℂ  n   : ( –| z  1 | 2  + | z  2 | 2 )  k   + ∑  i  s   =3  | z i  | 2  – ∑  i  n   =   s   +1  | z i  | 2  &lt; 1}, where  k  ∈ ℤ + , 3 ≤  s  ≤  n , and let  M ( n ,  s ,  k ) = ∂ D ( n ,  s ,  k ). We determine for any values of  n ,  s  and  k  the biholomorphic automorphisms of  D ( n ,  s ,  k ), identifying, in suitable cases, the germs of biholomorphisms that map  M ( n ,  s ,  k ) and  D ( n ,  s ,  k ) respectively in themselves. It turns out that, if  k  is even and  s  =  n , any such germ extends to a biholomorphic automorphism of  D ( n ,  s ,  k ), while, in other cases, it is a branch of an algebraic correspondence.

Localization of automorphisms of some unbounded Levi degenerate algebraic hypersurfaces in ℂ n