Tohoku Mathematical Journal

On linear deformations of Brieskorn singularities of two variables into generic maps

Kazumasa Inaba, Masaharu Ishikawa, Masayuki Kawashima, and Tat Thang Nguyen

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Abstract

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.

Article information

Source
Tohoku Math. J. (2), Volume 69, Number 1 (2017), 85-111.

Dates
First available in Project Euclid: 26 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1493172130

Digital Object Identifier
doi:10.2748/tmj/1493172130

Mathematical Reviews number (MathSciNet)
MR3640016

Zentralblatt MATH identifier
1376.57033

Subjects
Primary: 57R45: Singularities of differentiable mappings
Secondary: 58C27 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]

Keywords
Stable map higher differential mixed polynomial

Citation

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


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