A Second Main Theorem of Nevanlinna Theory for Closed Subschemes in Subgeneral Position

被引：1

作者：

Yu, Guangsheng ^{[1
]}

机构：

[1] Ningbo Univ, Sch Math & Stat, Ningbo 315211, Zhejiang, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2022年 / 43卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Second main theorem; In general position; Closed subscheme; Seshadri constant; Schmidt's subspace theorem; Hyperbolicity; SUBSPACE THEOREM; HOLOMORPHIC-CURVES;

D O I：

10.1007/s11401-022-0346-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, by using Seshadri constants for subschemes, the author establishes a second main theorem of Nevanlinna theory for holomorphic curves intersecting closed subschemes in (weak) subgeneral position. As an application of his second main theorem, he obtain a Brody hyperbolicity result for the complement of nef effective divisors. He also give the corresponding Schmidt's subspace theorem and arithmetic hyperbolicity result in Diophantine approximation.

引用

页码：567 / 584

页数：18

共 23 条

[1]

Aroca J. M., 2018, Complex Analytic Desingularization, DOI [10.1007/978-4-431-49822-3, DOI 10.1007/978-4-431-49822-3]

[2]

Cartan H, 1933, Mathematica (Cluj), V7, P80

[3] The degenerated second main theorem and Schmidt's subspace theorem [J].

Chen ZhiHua ;

Ru Min ;

Yan QiMing .

SCIENCE CHINA-MATHEMATICS, 2012, 55 (07) :1367-1380

[4] Positivity and complexity of ideal sheaves [J].

Cutkosky, SD ;

Ein, L ;

Lazarsfeld, R .

MATHEMATISCHE ANNALEN, 2001, 321 (02) :213-234

[5]

Ellwood D., 2014, RESOLUTION SINGULAR

[6]

Hartshorne R., 1977, ALGEBRAIC GEOM, DOI [10.1007/978-1-4757-3849-0, DOI 10.1007/978-1-4757-3849-0]

[7] A generalized subspace theorem for closed subschemes in subgeneral position [J].

He, Yan ;

Ru, Min .

JOURNAL OF NUMBER THEORY, 2021, 229 :125-141

[8] A GENERALIZED SCHMIDT SUBSPACE THEOREM FOR CLOSED SUBSCHEMES [J].

Heier, Gordon ;

Levin, Aaron .

AMERICAN JOURNAL OF MATHEMATICS, 2021, 143 (01) :213-226

[9] On the degeneracy of integral points and entire curves in the complement of nef effective divisors [J].

Heier, Gordon ;

Levin, Aaron .

JOURNAL OF NUMBER THEORY, 2020, 217 :301-319

[10]

Matsumura H., 1986, Commutative Ring Theory

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