Explicit construction of graph invariant for strongly pseudoconvex compact 3-dimensional rational CR manifolds |
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Authors: | Hing Sun Luk Stephen S.T. Yau |
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Affiliation: | (1) Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;(2) Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, M/C 249, Chicago, IL 60607-7045, USA |
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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. |
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Keywords: | strongly pseudoconvex embeddable CR manifolds rational CR manifolds algebraic equivalence topological algebraic equivalence graph invariants. |
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