Some invariants of tubular hypersurfaces in $\mathbb C^2$

Holomorphic invariants of tubular hypersurfaces (tubes) over plane analytic curves are treated. Nonspherical Levi nondegenerate tubes over affine homogeneous curves are studied. Such surfaces are shown to be holomorphically equivalent if and only if they are affinely equivalent. Two problems concerning the description of locally specified homogeneous hypersurfaces in $\mathbb C^2$ are posed. The construction of the invariants is based on the reduction of the equation of a tubular hypersurface to Moser normal form. Some properties of this reduction are discussed.