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.
"The Formula for the Singularity of Szegö Kernel: II." Asian J. Math. 8 (2) 353 - 362, April, 2004.