Arnold's problem on monotonicity of the Newton number for surface singularities

• Brzostowski Szymon

  Faculty of Mathematics and Computer Science University of Łódź

• Krasiński Tadeusz

  Faculty of Mathematics and Computer Science University of Łódź

• Walewska Justyna

  Faculty of Mathematics and Computer Science University of Łódź

抄録

According to the Kouchnirenko Theorem, for a generic (meaning non-degenerate in the Kouchnirenko sense) isolated singularity 𝑓 its Milnor number 𝜇 (𝑓) is equal to the Newton number 𝜈 (𝚪₊(𝑓)) of a combinatorial object associated to 𝑓, the Newton polyhedron 𝚪₊ (𝑓). We give a simple condition characterizing, in terms of 𝚪₊ (𝑓) and 𝚪₊ (𝑔), the equality 𝜈 (𝚪₊(𝑓)) = 𝜈 (𝚪₊(𝑔)), for any surface singularities 𝑓 and 𝑔 satisfying 𝚪₊ (𝑓) ⊂ 𝚪₊ (𝑔). This is a complete solution to an Arnold problem (No. 1982-16 in his list of problems) in this case.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 71 (4), 1257-1268, 2019

  一般社団法人 日本数学会

キーワード

• Arnold's problem
• Milnor number
• non-degenerate singularity
• Newton polyhedron

詳細情報

• CRID: 1390564227327674624
• NII論文ID: 130007733382
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/78557855
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 030030216
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I030030216
• 本文言語コード: en
• データソース種別:
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  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可