Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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

Similar Articles

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

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

Additional Information

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia