Defining equations for real analytic real hypersurfaces in ${\bf C}\sp n$

Abstract

A defining function for a real analytic real hypersurface can be uniquely written as 2 Ke(H) + E, where H is holomorphic and E contains no pure terms. We study how H and E change when we perform a local biholomorphic change of coordinates, or multiply by a unit. One of the main results is necesary and sufficient conditions on the first nonvanishing homogeneous part of E (expanded in terms of H) beyond £?oo that serve as obstructions to writing a defining equation as 2 Re(fe) + e, where e is independent of h. We also find necessary pluriharmonic obstructions to doing this, which arise from the easier case of attempting to straighten the hypersurface.