Pencil genus for normal surface singularities

• Tomaru Tadashi

  School of Health Sciences, Gunma University

抄録

Let (X,o) be a normal complex surface singularity. We define an invariant p_e(X,o) for (X,o) in terms of pencils of compact complex curves. Similarly, for a pair of (X,o) and h∈$¥mathfrak m$_X,o (the maximal ideal of $¥mathscr{O}$_X,o), we define an invariant p_e(X,o,h). We call p_e(X,o) (resp. p_e(X,o,h)) the pencil genus of (X,o) (resp. a pair of (X,o) and h). In this paper, we give a method to construct pencils of compact complex curves by gluing a resolution space of (X,o) and resolution spaces of some cyclic quotient singularities. Using this, we prove some formulae on p_e(X,o,h) and estimate p_e(X,o). We also characterize Kodaira singularities in terms of p_e(X,o,h).

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 59 (1), 35-80, 2007

  一般社団法人 日本数学会

キーワード

• surface singularities
• pencils of curves
• Kodaira singularities

詳細情報

• CRID: 1390001205116317696
• NII論文ID: 10019540487
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/1180135500
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2302662
• NDL書誌ID: 8612721
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I8612721
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用不可