## 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

### Citations:

Zbl 0237.32011; Zbl 0357.32014
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