Normal Forms and Degenerate CR Singularities

Abstract

Let (z, w) be the coordinates in C 2 . We construct a normal form for a class of real formal surfaces M ⊂ C 2 defined near a degenerate CR singularity p = 0 as follows, where P (z, z) is a real-valued homogeneous polynomial in (z, z) of degree k 0 ≥ 3 such that the coefficients of z k 0 and z k 0 are vanishing.