| Autor: |
Daniel Barlet, Jón Magnússon |
| Jazyk: |
angličtina |
| Rok vydání: |
2004 |
| Předmět: |
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| Zdroj: |
Asian J. Math. 8, no. 1 (2004), 173-214 |
| Popis: |
The main purpose of this article is to increase the efficiency of the tools introduced in [B.Mg. 98] and [B.Mg. 99], namely integration of meromorphic cohomology classes, and to generalize the results of [B.Mg. 99]. They describe how positivity conditions on the normal bundle of a compact complex submanifold Y of codimension n + 1 in a complex manifold Z can be transformed into positivity conditions for a Cartier divisor in a space parametrizing n-cycles in Z . ¶ As an application of our results we prove that the following problem has a positive answer in many cases : ¶ Let Z be a compact connected complex manifold of dimension n+p. Let Y ⊂ Z a submanifold of Z of dimension p-1 whose normal bundle N Y|Z is (Griffiths) positive. We assume that there exists a covering analytic family (X s ) s∈S of compact n-cycles in Z parametrized by a compact normal complex space S. ¶ Is the algebraic dimension of Z ≥ p ? |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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