Reducible hyperplane sections I Dedicated to the memory of our friend and colleague, Michael Schneider

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In this article we begin the study of \hat{X}, an n-dimensional algebraic submanifold of complex projective space \bm{P}<SUP>N</SUP>, in terms of a hyperplane section A which is not irreducible. A number of general results are given, including a Lefschetz theorem relating the cohomology of \hat{X} to the cohomology of the components of a normal crossing divisor which is ample, and a strong extension theorem for divisors which are high index Fano fibrations. As a consequence we describe \hat{X}=\bm{P}<SUP>N</SUP> of dimension at least five if the intersection of \hat{X} with some hyperplane is a union of r≥q 2 smooth normal crossing divisors \hat{A<SUB>1</SUB>}, ..., \hat{A<SUB>r</SUB>}, such that for each i, h<SUP>1</SUP>(\mathcal{O}_{\hat{A<SUB>i</SUB>}}) equals the genus g(\hat{A<SUB>i</SUB>}) of a curve section of \hat{A<SUB>i</SUB>}. Complete results are also given for the case of dimension four when r=2.

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  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 51(4), 887-910, 1999-10-01 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10004480899
  • 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
    4894970
  • 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  CJP引用  NDL  J-STAGE 
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