On holomorphic curves in algebraic varieties with ample irregularity
On holomorphic curves in algebraic varieties with ample irregularity
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具有充分不规则性的代数簇的全纯曲线
DOI：
10.1007/bf01390205
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发表时间：
1977
影响因子：
3.1
通讯作者：
T. Ochiai
中科院分区：
文献类型：
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作者：
T. Ochiai
当X是曲面时，他只给出了(1-1)的粗略证明，一般情况留给读者。然而，即使他对表面的粗略证明本身也存在严重的缺陷。值得注意的是 (i) 他本人在论文中承认，他的引理 III 没有得到足够的普遍性证明来支持他的论点（参见[2, p. 22]）。事实上，我们已经使用[3]中的结果证明了这个引理III。下一个反对意见 (ii) 是他的证明中的一个基本步骤（即下面的 (3-1) 为真）被忽略了，根本没有被证明。正如我们所看到的最后一步，它非常重要，以至于我们还不知道这一步的有效性，除了 X 是表面的情况。还有-AMS（MOS）学科分类（1970）。初级32C10、30A70；中学 14K20。
He only gives a sketchy proof to (1-1) when X is a surface, and the general case is left to the reader. However, even his rough proof for surfaces, in itself, contains serious gaps. Notably (i) he himself admits in his paper that his Lemma III is not proved in enough generality to support his argument (cf.[2, p. 22]). In fact we have proved this Lemma III using results in [3]. The next objection (ii) is that one of the essential steps in his proof (ie, that (3-1) below is true) is overlooked and not proved at all. As we see this last step, it is so highly nontrivial that we do not know yet the validity of this step in general, except the case when X is a surface. There-AMS (MOS) subject classifications (1970). Primary 32C10, 30A70; Secondary 14K20.