Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties
Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties
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代数簇中对数导数和全纯曲线的引理
DOI：
10.1017/s0027763000019504
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发表时间：
1981
影响因子：
0.8
通讯作者：
J. Noguchi
中科院分区：
文献类型：
--
作者：
J. Noguchi
Nevanlinna关于对数导数的引理在复平面C上的亚纯函数的第二个主要定理的证明中发挥了重要作用（参见，例如，在一个实施例中，[17]）。在[19]中，引理2.3推广到紧致复流形M中的整条全纯曲线f：C → M（[19]中的引理2.3对非Kähler M仍然有效）。在这里，我们一般把从C或黎曼曲面的区域到M的全纯映射称为M中的全纯曲线，如果没有混淆的话，有时也用它的象的意义。将上述关于对数导数的广义引理应用于复射影代数光滑簇V中的全纯曲线f：C → V，并利用Ochiai [22，定理A]，我们得到了关于f与V上的因子的第二主要定理型不等式（见[19，主要定理]和[20]）。Nevanlinna引理在对数导数上的其他推广由Nevanlinna [16]，Griffiths-King [10，§ 9]和Vitter [23]得到。
Nevanlinna’s lemma on logarithmic derivatives played an essential role in the proof of the second main theorem for meromorphic functions on the complex plane C (cf., e.g., [17]). In [19, Lemma 2.3] it was generalized for entire holomorphic curves f: C → M in a compact complex manifold M (Lemma 2.3 in [19] is still valid for non-Kähler M). Here we call, in general, a holomorphic mapping from a domain of C or a Riemann surface into M a holomorphic curve in M, and sometimes use it in the sense of its image if no confusion occurs. Applying the above generalized lemma on logarithmic derivatives to holomorphic curves f: C → V in a complex projective algebraic smooth variety V and making use of Ochiai [22, Theorem A], we had an inequality of the second main theorem type for f and divisors on V (see [19, Main Theorem] and [20]). Other generalizations of Nevanlinna’s lemma on logarithmic derivatives were obtained by Nevanlinna [16], Griffiths-King [10, § 9] and Vitter [23].