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 CN. 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 ⊕k=0∞ mk/mk+1, where m is the maximal ideal of each singularity. An example is computed explicitly to demonstrate how the algorithms work.