Real Seifert form determines the spectrum for semiquasihomogeneous hypersurface singularities in \bm{C}<SUP>3</SUP>

• SAEKI Osamu

  Department of Mathematics Faculty of Science Hiroshima University

Bibliographic Information

Other Title

• Real Seifert form determines the spectrum for semiquasihomogeneous hypersurface singularities in C3
• To the memory of Professor Etsuo Yoshinaga

Abstract

We show that the real Seifert form determines the weights for nondegenerate quasihomogeneous polynomials in \bm{C}³. Consequently the real Seifert form determines the spectrum for semiquasihomogeneous hypersurface singularities in \bm{C}³. As a corollary, we obtain the topological invariance of weights for nondegenerate quasihomogeneous polynomials in \bm{C}³, which has already been proved by the author [{Sae1}] and independently by Xu and Yau [{Ya1}], [{Ya2}], [{XY1}], [{XY2}]. The method in this paper is totally different from their approaches and gives some new results, as corollaries, about holomorphic function germs in \bm{C}³ which are connected by μ-constant deformations to nondegenerate quasihomogeneous polynomials. For example, we show that two semiquasihomogeneous functions of three complex variables have the same topological type if and only if they are connected by a μ-constant deformation.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 52 (2), 409-431, 2000

  The Mathematical Society of Japan

Keywords

• Real Seifert form
• quasihomogeneous polynomial
• weights
• spectrum
• μ-constant deformation

Details

• CRID: 1390282680092713088
• NII Article ID: 10004480298
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/05220409
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 1742796
• NDL BIB ID: 5374857
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I5374857
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed