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

Kazumasa Inaba; Masaharu Ishikawa; Masayuki Kawashima; Tat Thang Nguyen

doi:10.2748/tmj/1493172130

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

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

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	85-111
Number of pages	27
Journal	Tohoku Mathematical Journal
Volume	69
Issue number	1
DOIs	https://doi.org/10.2748/tmj/1493172130
Publication status	Published - 2017 Mar
Externally published	Yes

Keywords

Higher differential
Mixed polynomial
Stable map

ASJC Scopus subject areas

Mathematics(all)

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10.2748/tmj/1493172130

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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.",

keywords = "Higher differential, Mixed polynomial, Stable map",

author = "Kazumasa Inaba and Masaharu Ishikawa and Masayuki Kawashima and Nguyen, {Tat Thang}",

year = "2017",

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AU - Inaba, Kazumasa

AU - Ishikawa, Masaharu

AU - Kawashima, Masayuki

AU - Nguyen, Tat Thang

PY - 2017/3

Y1 - 2017/3

N2 - 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.

AB - 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.

KW - Higher differential

KW - Mixed polynomial

KW - Stable map

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JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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