Let M be a strongly pseudoconvex hypersurface in Cn+1, i.e. the boundary of a
domain Ω in Cn+1. The Szegö kernel KS(x, y), x,y ∈ M, is smooth outside of the
diagonal x = y. The singularity at (x, x) is determined by the local datum at x of M,
even though KS itself is a global object. Our problem is to write down the singularity
at (x, x) in terms of the local equation of M in Cn+1. We fix a reference point, say
p*, in M and only consider the germ of M at p*. Hence we we may shrink M near
p* without mentioning it. We use as the model structure the boundary of the Siegel
upper half space.