Reducible hyperplane sections I Dedicated to the memory of our friend and colleague, Michael Schneider
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概要
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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.
- 社団法人 日本数学会の論文
- 1999-10-01
著者
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Sommese Andrew
Department Of Mathematics University Of Notre Dame
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Sommese Andrew
Department Of Mathematics
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Chandler Karen
Department Of Mathematics University Of Notre Dame
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HOWARD Alan
Department of Mathematics University of Notre Dame
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- New properties of special varieties arising from adjunction theory
- A remark on the Kawamata rationality theorem
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- Reducible hyperplane sections I Dedicated to the memory of our friend and colleague, Michael Schneider
- A remark on the Kawamata rationality theorem