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CR singularities of real fourfolds in \(\mathbb C^{3}\). (English) Zbl 1233.32027
The author studies embedded real \(4\)-manifolds into complex \(3\)-space. Points where the tangent space of the \(4\)-manifold is a complex \(2\)-plane are called CR-singular. The main result of the paper is the classification of the quadratic part of the CR-singularities up to local holomorphic coordinate changes. A table of normal forms is presented. It is also shown how the quadratic part determines the intersection index, an enumerative invariant occurring in global formulas.

MSC:
32V40 Real submanifolds in complex manifolds
15A21 Canonical forms, reductions, classification
32S05 Local complex singularities
32S20 Global theory of complex singularities; cohomological properties
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