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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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 $ {X_q}$ 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: http://dx.doi.org/10.1090/S0002-9947-1978-0492307-X
PII: S 0002-9947(1978)0492307-X
Keywords: Nonreduced complex space, cartesian product, derivations, complex analytic isomorphism, reduced singularity
Article copyright: © Copyright 1978 American Mathematical Society