Singularity theory is not a field in itself, but rather an
application of algebraic geometry, analytic geometry and
differential analysis. The adjective 'singular' in the title refers
here to singular points of complex-analytic or algebraic varieties
or mappings. A tractable (and very natural) class of singularities
to study are the isolated complete intersection singularities, and
much progress has been made over the past decade in understanding
these and their deformations.
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