Isosingular loci and the Cartesian product structure of complex analytic singularities

Author:
Robert Ephraim

Journal:
Trans. Amer. Math. Soc. **241** (1978), 357-371

MSC:
Primary 32B10; Secondary 32C40

DOI:
https://doi.org/10.1090/S0002-9947-1978-0492307-X

MathSciNet review:
492307

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Abstract: Let *X* be a (not necessarily reduced) complex analytic space, and let *V* be a germ of an analytic space. The locus of points *q* in *X* at which the germ is complex analytically isomorphic to *V* is studied. If it is nonempty it is shown to be a locally closed submanifold of *X*, and *X* is locally a Cartesian product along this submanifold. This is used to define what amounts to a coarse partial ordering of singularities. This partial ordering is used to show that there is an essentially unique way to completely decompose an arbitrary reduced singularity as a cartesian product of lower dimensional singularities. This generalizes a result previously known only for irreducible singularities.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1978-0492307-X

Keywords:
Nonreduced complex space,
cartesian product,
derivations,
complex analytic isomorphism,
reduced singularity

Article copyright:
© Copyright 1978
American Mathematical Society