On the Seifert form at infinity associated with polynomial maps

• NÉMETHI András

  Department of Mathematics The Ohio State University

抄録

If a polynomial map f:Cⁿ→ C has a nice behaviour at infinity (e.g. it is a“good polynomial”), then the Milnor fibration at infinity exists, in particular, one can define the Seifert form at infinity Γ(f) associated with f. In this paper we prove a Sebastiani-Thom type formula. Namely, if f:Cⁿ→ C and g:C^m→ C are“good”polynomials, and we define h=f+g:C^n+m→ C by h(x, y)=f(x)+g(y), then Γ(h)=(-1)^mnΓ(f) Γ(g). This is the global analogue of the local result, proved independently by K. Sakamoto and P. Deligne for isolated hypersurface singularities.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 51 (1), 63-70, 1999

  一般社団法人 日本数学会

キーワード

• Good polynomials
• Milnor fibrations at infinity
• Seifert forms
• variation map
• spinnable structures
• open book decomposition

詳細情報

• CRID: 1390282680092798464
• NII論文ID: 10002151375
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/05110063
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 1660996
• NDL書誌ID: 4643265
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I4643265
• 本文言語コード: en
• データソース種別:
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