Explicit construction of graph invariant for strongly pseudoconvex compact 3-dimensional rational CR manifolds

Abstract

Let X be a strongly pseudoconvex compact 3-dimensional CR manifolds which bounds a complex variety with isolated singularities in some C$^N$. The weighted dual graph of the exceptional set of the minimal good resolution of V is a CR invariant of X; in case X has a tranversal holomorphic S¹ action, we show that it is a complete topological invariant of except for two special cases. When X is a rational CR manifolds, we give explicit algebraic algorithms to compute the graph invariant in terms of the ring structure of [oplus ]$_k=0$$^$∞ m$^k$/m$^k+1$, where m is the maximal ideal of each singularity. An example is computed explicitly to demonstrate how the algorithms work.