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

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


A characterization of semi-quasihomogeneous functions in terms of the Milnor number

Authors: Masako Furuya and Masataka Tomari
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1885-1890
MSC (2000): Primary 14B05; Secondary 13H15, 32S05
Published electronically: January 7, 2004
MathSciNet review: 2053957
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give an inequality on the Milnor number $\mu (f)$ of a hypersurface isolated singularity in terms of the weighted Taylor expansion $ f = f_{\rho }+ f_{\rho +1} + \cdots $ for a given weight on the coordinates. Here the equality holds if and only if the leading term $f_{\rho }$ defines an isolated singularity. This gives a characterization of the semi-quasihomogeneous condition in terms of $\mu $. Our proof uses a result on multiplicity of filtered rings and is given by purely algebraic arguments.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14B05, 13H15, 32S05

Retrieve articles in all journals with MSC (2000): 14B05, 13H15, 32S05

Additional Information

Masako Furuya
Affiliation: 2-155, Makinohara, Matsudo-city, Chiba, 270-2267, Japan

Masataka Tomari
Affiliation: Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya, Tokyo, 156-0045, Japan

PII: S 0002-9939(04)07383-6
Keywords: Milnor number, semi-quasihomogeneous function, multiplicity of local rings, filtered rings
Received by editor(s): June 28, 2001
Received by editor(s) in revised form: March 15, 2003
Published electronically: January 7, 2004
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 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