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CR-geometry and deformations of isolated singularities. (English) Zbl 0871.32023

Mem. Am. Math. Soc. 597, 96 p. (1997).
The authors show how to compute the parameter space \(X\) for the versal deformation of an isolated singularity \((V,0)\), whose existence was shown by H. Grauert [Invent. Math. 15, 171-198 (1972; Zbl 0237.32011)], under the assumption \(\dim V\geq 4\), \(\text{depth}_{\{0\}}V \geq 3\), from the CR-structure on a link \(M\) of the singularity.
They do this by showing that the space \(X\) is isomorphic to the space (denoted here by \(K_M)\) associated to \(M\) by M. Kuranishi [Proc. Symp. Pure Math. 30, 97-106 (1977; Zbl 0357.32014)]. In fact, they produce isomorphisms of the associated complete local rings by producing quasi-isomorphisms of the controlling differential graded Lie algebras for the corresponding formal deformation theories.

MSC:

32S30 Deformations of complex singularities; vanishing cycles
32V05 CR structures, CR operators, and generalizations
14B12 Local deformation theory, Artin approximation, etc.
32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
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