Birationality of the automorphisms of the model surface

We will discuss that the group of holomorphic automorphisms of holomorphically homogeneous nondegenerate (finite Bloom–Graham type + holomorphic nondegenaracy) model surface is a subgroup of the group of birational automorphisms of the ambient space (Cremona group) with uniformly bounded degree. We will give an estimate of the degree of the automorphisms in terms of the dimension of the ambient space.