Meromorphic mappings of a covering space over $C\spm$ into a projective variety and defect relations
Meromorphic mappings of a covering space over $C\spm$ into a projective variety and defect relations
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$Cspm$ 上覆盖空间的亚纯映射到射影簇和缺陷关系
DOI：
10.32917/hmj/1206136323
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发表时间：
1976
影响因子：
0.2
通讯作者：
J. Noguchi
中科院分区：
文献类型：
--
作者：
J. Noguchi
Carlson-Griffiths [1]和Griffiths-King [4]研究了从光滑仿射簇A到光滑射影簇V的全纯映射的值分布，建立了从A到V的全纯映射的Nevanlinna第二主要定理和亏损关系。本文研究了从X到V的亚纯映射的值分布，其中X是有限解析覆盖X-？-> C（见第2节定义1）。主要目的是证明从X到F的亚纯映射的Nevanlinna第二主要定理和Griffiths-King型亏损关系（见第6节定理1和定理2）。[4]）。下一节将专门介绍符号和术语。在第三节中，我们将证明关于X上正电流的两个预备引理。在第4节中，我们将把Selberg [12]中的分歧估计推广到有限解析覆盖X → C的情况（引理4.1）。这一估计以及Carlson-Griffiths [1]和Griffiths-King [4]构造的V上的奇异体积形式的使用将对获得第6节中的第二个主要定理起重要作用。在第5节中，我们将研究亚纯映射/：X-+ V的真存在域。这一研究将使第4节中得到的分歧估计有可能应用于第二个主要定理的证明。在同一节中，我们将证明亚纯映射f：X-> F关于正的线丛L->F的特征函数T（r，L）满足
Carlson-Griffiths [1] and Griffiths-King [4] studied the value distribution of holomorphic mappings from a smooth affine variety A into a smooth projective variety V. Among others, they established Nevanlinna's second main theorem and defect relation for holomorphic mappings from A into V. Recently, these results were generalized to the case of meromorphic mappings by Shiίfman [13]. In the present paper we study the value distribution of meromorphic mappings from X into V, where X is the complex space of a finite analytic covering X—?-> C (see Definition 1 in section 2). The main purpose is to show Nevanlinna's second main theorem and defect relation of Griffiths-King's type for meromorphic mappings from X into F(see Theorems 1 and 2 in section 6 and cf. [4]). The next section will be devoted to the notation and terminologies. In section 3 we shall prove two preparatory lemmas concerning positive currents on X. In section 4 we shall generalize the ramification estimate in Selberg [12] to the case of the finite analytic covering X — -» C (Lemma 4.1). This estimate and the use of a singular volume form on V constructed by Carlson-Griffiths [1] and Griffiths-King [4] will play essential roles to obtain the second main theorem in section 6. In section 5 we shall investigate the proper domain of existence of a meromorphic mapping /: X-+V. This investigation will make the ramification estimate, obtained in section 4, possible to apply to the proof of the second main theorem. In the same section we shall prove that the characteristic function T(r, L) of a meromorphic mapping/: X-»Fwith respect to a positive line bundle L->F(see section 3 for the definition) satisfies