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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A case in which irreducibility of an analytic germ implies irreducibility of the tangent cone


Author: Richard Draper
Journal: Proc. Amer. Math. Soc. 39 (1973), 443-449
MSC: Primary 32B10; Secondary 32C40
MathSciNet review: 0316744
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Abstract: There are simple examples in which a variety is irreducible at a point but has a reducible tangent cone. The following theorem is proved. If $ {X_p}$ is an irreducible analytic germ and if the Jacobian ideal beomes principal on the normalization then the tangent cone of $ X$ at $ p$ is irreducible. If, moreover, the singular set of $ X$ is a manifold at $ p$ then $ X$ is Whitney $ a,b$-regular along the singular set at $ p$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0316744-X
PII: S 0002-9939(1973)0316744-X
Keywords: Tangent cone, Jacobian ideal, normalization, Whitney $ a,b$-regularity
Article copyright: © Copyright 1973 American Mathematical Society