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)

Request Permissions   Purchase Content 
 

 

Lipschitz regular complex algebraic sets are smooth


Authors: L. Birbrair, A. Fernandes, D. T. Lê and J. E. Sampaio
Journal: Proc. Amer. Math. Soc. 144 (2016), 983-987
MSC (2010): Primary 14B05; Secondary 32S50
DOI: https://doi.org/10.1090/proc/12783
Published electronically: September 1, 2015
MathSciNet review: 3447652
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A classical theorem of Mumford implies that a topologically regular complex algebraic surface in $ \mathbb{C}^3$ with an isolated singular point is smooth. We prove that any Lipschitz regular complex algebraic set is smooth. No restriction on the dimension and no restriction on the singularity to be isolated is needed.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14B05, 32S50

Retrieve articles in all journals with MSC (2010): 14B05, 32S50


Additional Information

L. Birbrair
Affiliation: Departamento de Matemática, Universidade Federal do Ceará Av. Humberto Monte, s/n Campus do Pici - Bloco 914, 60455-760 Fortaleza-CE, Brazil
Email: birb@ufc.br

A. Fernandes
Affiliation: Departamento de Matemática, Universidade Federal do Ceará Av. Humberto Monte, s/n Campus do Pici - Bloco 914, 60455-760 Fortaleza-CE, Brazil
Email: alexandre.fernandes@ufc.br

D. T. Lê
Affiliation: Departamento de Matemática, Universidade Federal do Ceará Av. Humberto Monte, s/n Campus do Pici - Bloco 914, 60455-760 Fortaleza-CE, Brazil
Email: ledt@ictp.it

J. E. Sampaio
Affiliation: Departamento de Matemática, Universidade Federal do Ceará Av. Humberto Monte, s/n Campus do Pici - Bloco 914, 60455-760 Fortaleza-CE, Brazil
Email: edsonsampaio@mat.ufc.br

DOI: https://doi.org/10.1090/proc/12783
Keywords: Lipschitz regular point, algebraic sets
Received by editor(s): April 30, 2014
Received by editor(s) in revised form: September 3, 2014, February 19, 2015, and March 13, 2015
Published electronically: September 1, 2015
Additional Notes: The first and second authors were partially supported by CAPES-COFECUB and by CNPq-Brazil, grants no. 302655/2014-0 and 302764/2014-3, respectively. The fourth author was partially supported by FUNCAP
Communicated by: Michael Wolf
Article copyright: © Copyright 2015 American Mathematical Society