Real Seifert form determines the spectrum for semiquasihomogeneous hypersurface singularities in C^3

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We show that the real Seifert form determines the weights for nondegenerate quasihomogeneous polynomials in \bm{C}<SUP>3</SUP>. Consequently the real Seifert form determines the spectrum for semiquasihomogeneous hypersurface singularities in \bm{C}<SUP>3</SUP>. As a corollary, we obtain the topological invariance of weights for nondegenerate quasihomogeneous polynomials in \bm{C}<SUP>3</SUP>, 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}<SUP>3</SUP> 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.

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  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 52(2), 409-431, 2000-04 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10004480298
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    5374857
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  J-STAGE 
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