On Innermost Circles of the Sets of Singular Values for Generic Deformations of Isolated Singularities

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We will show that for each k≠1, there exists an isolated singularity of a real analytic map from ℝ4 to ℝ2 which admits a real analytic deformation such that the set of singular values of the deformed map has a simple, innermost component with k outward cusps and no inward cusps. Conversely, such a singularity does not exist if k=1.

Original languageEnglish
Pages (from-to)237-247
Number of pages11
JournalActa Mathematica Vietnamica
Volume42
Issue number2
DOIs
Publication statusPublished - 2017 Jun 1
Externally publishedYes

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Isolated Singularity
Cusp
Singular Values
Circle
Singularity

Keywords

  • Critical value
  • Excellent map
  • Higher differential
  • Mixed polynomial
  • Stable map

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On Innermost Circles of the Sets of Singular Values for Generic Deformations of Isolated Singularities. / Inaba, Kazumasa; Ishikawa, Masaharu; Kawashima, Masayuki; Thang, Nguyen Tat.

In: Acta Mathematica Vietnamica, Vol. 42, No. 2, 01.06.2017, p. 237-247.

Research output: Contribution to journalArticle

Inaba, Kazumasa ; Ishikawa, Masaharu ; Kawashima, Masayuki ; Thang, Nguyen Tat. / On Innermost Circles of the Sets of Singular Values for Generic Deformations of Isolated Singularities. In: Acta Mathematica Vietnamica. 2017 ; Vol. 42, No. 2. pp. 237-247.
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