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 journalArticle

1 Citation (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 languageEnglish
Pages (from-to)85-111
Number of pages27
JournalTohoku Mathematical Journal
Volume69
Issue number1
DOIs
Publication statusPublished - 2017 Mar 1
Externally publishedYes

Fingerprint

Cusp
Singularity
Fold
Polynomial Maps
Complex Variables
Term
Corollary
Polynomial
Estimate

Keywords

  • Higher differential
  • Mixed polynomial
  • Stable map

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On linear deformations of Brieskorn singularities of two variables into generic maps. / Inaba, Kazumasa; Ishikawa, Masaharu; Kawashima, Masayuki; Nguyen, Tat Thang.

In: Tohoku Mathematical Journal, Vol. 69, No. 1, 01.03.2017, p. 85-111.

Research output: Contribution to journalArticle

Inaba, Kazumasa ; Ishikawa, Masaharu ; Kawashima, Masayuki ; Nguyen, Tat Thang. / On linear deformations of Brieskorn singularities of two variables into generic maps. In: Tohoku Mathematical Journal. 2017 ; Vol. 69, No. 1. pp. 85-111.
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