Contents Online

# Asian Journal of Mathematics

## Volume 8 (2004)

### Number 2

### The Formula for the Singularity of Szegö Kernel: II

Pages: 353 – 362

DOI: http://dx.doi.org/10.4310/AJM.2004.v8.n2.a8

#### Author

#### Abstract

Let ** M** be a strongly pseudoconvex hypersurface in C^{n+1}, i.e. the boundary of a domain Ω in C^{n+1}. The Szegö kernel *K*^{S}*(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 K^{S} 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 C^{n+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.