Compositio Mathematica

Table of Contents - 1998 - Volume 114, Issue 01  


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

HING SUN LUK a1 and STEPHEN S.T. YAU a2
a1 Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong; e-mail: hsluk@math.cuhk.edu.hk
a2 Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, M/C 249, Chicago, IL 60607-7045, USA; e-mail: yau@uic.edu

Article author query
luk hs   [Google Scholar] 
yau ss   [Google Scholar] 
 

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 B: plus sign in circle]$_k=0$$^$[infty infinity] m$^k$/m$^k+1$, where m is the maximal ideal of each singularity. An example is computed explicitly to demonstrate how the algorithms work.


Key Words: strongly pseudoconvex embeddable CR manifolds; rational CR manifolds; algebraic equivalence; topological algebraic equivalence; graph invariants..