A short analytic proof of closedness of logarithmic forms
A short analytic proof of closedness of logarithmic forms
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对数形式封闭性的简短解析证明
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
J. Noguchi
中科院分区：
文献类型：
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作者：
J. Noguchi
Deligne[D，(3.2.14)]通过证明一些谱序列的简并性，证明了光滑复拟射影簇上对数形式的d-闭性。实际上，他的证明适用于紧致Kahler流形的Zariski开子空间。对数形式在解析-代数几何的各个方面都起着重要的作用，包括全纯映射的值分布(例如，参见[D]、[I]、[NL]、[N2]、[N3]和[N4])，而它们的闭性是基本的。因此，仅基于经典调和积分理论[K]给出它的简短证明可能是有价值的，也是我们的目的所在。
Deligne [D, (3.2.14)] proved the d-closedness of logarithmic forms on a smooth complex quasi-projective variety by showing the degeneracy of some spectral sequence. Actually, his proof works for a Zariski open subspace of a compact Kahler manifold. The logarithmic forms play important roles in various aspects of analytic-algebraic geometry, including the value distribution of holomorphic mappings (see, e.g., [D], [I], [Nl], [N2], [N3] and [N4]), and their closedness is fundamental. Therefore it may be of worth, and hence our purpose of this note to give its short proof based only on the classical harmonic integral theory [K].