Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 69, Number 1 (2017), 85-111.
On linear deformations of Brieskorn singularities of two variables into generic maps
In this paper, we study deformations of Brieskorn polynomials of two variables obtained by adding linear terms consisting of the conjugates of complex variables and prove that the deformed polynomial maps have only indefinite fold and cusp singularities in general. We then estimate the number of cusps appearing in such a deformation. As a corollary, we show that a deformation of a complex Morse singularity with real linear terms has only indefinite folds and cusps in general and the number of cusps is 3.
Tohoku Math. J. (2), Volume 69, Number 1 (2017), 85-111.
First available in Project Euclid: 26 April 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R45: Singularities of differentiable mappings
Secondary: 58C27 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
Inaba, Kazumasa; Ishikawa, Masaharu; Kawashima, Masayuki; Nguyen, Tat Thang. On linear deformations of Brieskorn singularities of two variables into generic maps. Tohoku Math. J. (2) 69 (2017), no. 1, 85--111. doi:10.2748/tmj/1493172130. https://projecteuclid.org/euclid.tmj/1493172130