Théorie des résidus de Leray et formes de Barlet sur une intersection complète singulière

Aleksandr G. Aleksandrov, Avgust K. Tsikh
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引用次数: 24

Abstract

Let S be a complex analytic manifold and CS a reduced complete intersection. We construct a complex ΩS(logC) of sheaves of the so-called multi-logarithmic differential forms on S with respect to C and define a residue map resS(logC)→ωC from this complex onto the Barlet complex ωC of regular meromorphic differential forms on C. The residue map is proved to be a natural morphism between the two complexes; it follows then that sections of the complex ωC may be regarded as a generalization of the residue differential forms defined by Leray. Moreover, we show that the map res can be given explicitly in terms of a certain integration current.

奇异完全交点上的Leray残差理论和Barlet形式
设S是一个复解析流形,C∧S是一个简化的完全交集。我们构造了S上关于C的所谓多对数微分形式的束的复合体ΩS•(logC),并定义了一个残差映射res:ΩS•(logC)→ωC•从这个复合体到C上正则亚纯微分形式的Barlet复合体ωC•,证明了残差映射是两个复合体之间的自然态射;因此,复ωC•的部分可以看作是Leray定义的剩余微分形式的推广。此外,我们还证明了映射值可以用一定的积分电流来明确地给出。
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