Skip Navigation


Proceedings of the London Mathematical Society Advance Access originally published online on February 18, 2008
Proceedings of the London Mathematical Society 2008 96(3):792-812; doi:10.1112/plms/pdn001
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow All Versions of this Article:
96/3/792    most recent
pdn001v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Zhitomirskii, M.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

Fully simple singularities of plane and space curves

M. Zhitomirskii

Department of Mathematics
Technion
32000 Haifa
Israel

Received 20 July 2005. Revision received 16 April 2007.

In this wor we introduce the definition of fully simple singularities of parameterized curves and explain that this definition is more natural than the definition of simple singularities. The set of fully simple singularities is much smaller than the set of simple ones. We determine and classify all fully simple singularities of plane and space curves, with any number of components. Our classification results imply that any fully simple singularity of a plane or a space curve is quasi-homogeneous (whereas there is a number of non-quasi-homogeneous simple singularities). Another outcome of our classification results is a one-to-one correspondence between the fully simple singularities of plane curves and the classical A-D-E singularities of functions.

2000 Mathematics Subject Classification 14B05, 14H50, 58K60.

The work on this paper was supported by the Israel ScienceFoundation, grant 1356/04.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.