Holomorphic curves in algebraic varieties of maximal albanese dimension
Holomorphic curves in algebraic varieties of maximal albanese dimension
复制标题
最大阿尔巴尼斯维数代数簇的全纯曲线
DOI：
10.1142/s0129167x15410062
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发表时间：
2015
影响因子：
0.6
通讯作者：
Katsutoshi Yamanoi
中科院分区：
文献类型：
--
作者：
Takekoshi;Tatsuya; Minamidani;Tetsuhiro; Komugi;Shinya; Kohno;Kotaro; Tosaki;Tomoka; Sorai;Kazuo; Muller;Erik; Mizuno;Norikazu; Kawamura;Akiko; Onishi;Toshikazu; Fukui;Yasuo; Ezawa;Hajime; Oshima;Tai; Scott;Kimberly S.; Austermann;Jason E.;;H. Tamura;Katsutoshi Yamanoi
证明了关于全纯曲线f：Y→X从复平面→ℂ的有限覆盖空间Yℂ到极大阿尔巴尼亚维复射影流形X的第二个主要定理估计.此外，如果X是一般类型的，则这意味着X的特殊集是X的真子集。对于这样的X中的射影曲线C，如果C不包含在X中的真例外子集中，我们的估计也得到了C的次数与C的几何亏格之比的一个上界。
We prove a second main theorem type estimate in Nevanlinna theory for holomorphic curves f : Y → X from finite covering spaces Y → ℂ of the complex plane ℂ into complex projective manifolds X of maximal albanese dimension. If X is moreover of general type, then this implies that the special set of X is a proper subset of X. For a projective curve C in such X, our estimate also yields an upper bound of the ratio of the degree of C to the geometric genus of C, provided that C is not contained in a proper exceptional subset in X.