A counterexample to the dimension conjecture (Q2460515)

Conjecture: For an arbitrary germ of real analytic surface of dimension \(d\) and codimension \(k\) without any nondegeneracy assumptions, the dimension of the local group either is infinite or does not exceed the maximal dimension of a model surface with the same dimension and codimension. This conjecture was proved for four- and five-dimensional surfaces in \(\mathbb{C}^3\). The author shows that the conjecture is false for nine-dimensional surfaces in \(\mathbb{C}^7\).