Lipschitz regular complex algebraic sets are smooth
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- by L. Birbrair, A. Fernandes, D. T. Lê and J. E. Sampaio
- Proc. Amer. Math. Soc. 144 (2016), 983-987
- DOI: https://doi.org/10.1090/proc/12783
- Published electronically: September 1, 2015
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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
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Bibliographic 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
- MR Author ID: 676391
- 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
- MR Author ID: 1144437
- Email: edsonsampaio@mat.ufc.br
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 983-987
- MSC (2010): Primary 14B05; Secondary 32S50
- DOI: https://doi.org/10.1090/proc/12783
- MathSciNet review: 3447652