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

Published online by Cambridge University Press:  04 December 2007

HING SUN LUK
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong; e-mail: [email protected]
STEPHEN S.T. YAU
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, M/C 249, Chicago, IL 60607-7045, USA; e-mail: [email protected]
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Abstract

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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.

Type
Research Article
Copyright
© 1998 Kluwer Academic Publishers