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 is an irreducible analytic germ and if the Jacobian ideal beomes principal on the normalization then the tangent cone of at is irreducible. If, moreover, the singular set of is a manifold at then is Whitney -regular along the singular set at .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0316744-X

Keywords:
Tangent cone,
Jacobian ideal,
normalization,
Whitney -regularity

Article copyright:
© Copyright 1973
American Mathematical Society