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2017 On linear deformations of Brieskorn singularities of two variables into generic maps
Kazumasa Inaba, Masaharu Ishikawa, Masayuki Kawashima, Tat Thang Nguyen
Tohoku Math. J. (2) 69(1): 85-111 (2017). DOI: 10.2748/tmj/1493172130

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.

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Kazumasa Inaba. Masaharu Ishikawa. Masayuki Kawashima. Tat Thang Nguyen. "On linear deformations of Brieskorn singularities of two variables into generic maps." Tohoku Math. J. (2) 69 (1) 85 - 111, 2017. https://doi.org/10.2748/tmj/1493172130

Information

Published: 2017
First available in Project Euclid: 26 April 2017

zbMATH: 1376.57033
MathSciNet: MR3640016
Digital Object Identifier: 10.2748/tmj/1493172130

Subjects:
Primary: 57R45
Secondary: 14B05 , 58C27

Keywords: higher differential , mixed polynomial , stable map

Rights: Copyright © 2017 Tohoku University

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Vol.69 • No. 1 • 2017
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