Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32B10, 32C40

Retrieve articles in all journals with MSC: 32B10, 32C40

Additional Information

Keywords: Tangent cone, Jacobian ideal, normalization, Whitney $ a,b$-regularity
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society