An effective function field version of Schmidt's subspace theorem for projective varieties, with arbitrary families of homogeneous polynomials

被引：6

作者：

Quang, Si Duc ^{[1
,2
]}

机构：

[1] Hanoi Natl Univ Educ, Dept Math, Cau Giay, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

[2] Thang Long Inst Math & Appl Sci, Hoang Mai, Hanoi, Vietnam

来源：

JOURNAL OF NUMBER THEORY | 2022年 / 241卷

关键词：

Effective subspace theorem; Function field; Diophantine approximation; Homogeneous polynomial; Chow weight;

D O I：

10.1016/j.jnt.2022.04.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, by giving a new lower bound estimate for the Chow weight of a projective variety, we will prove an effective Schmidt subspace theorem for projective varieties on the rational function field with arbitrary families of higher degree homogeneous polynomials. Our result is a generalization and also an improvement of the previous results.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：563 / 580

页数：18

共 13 条

[1] Quantitative subspace theorem and general form of second main theorem for higher degree polynomials [J].

Duc Quang Si .

MANUSCRIPTA MATHEMATICA, 2022, 169 (3-4) :519-547

[2] A generalization of the Subspace Theorem with polynomials of higher degree [J].

Evertse, Jan-Hendrik ;

Ferretti, Roberto G. .

DIOPHANTINE APPROXIMATION: FESTSCHRIFT FOR WOLFGANG SCHMIDT, 2008, 16 :175-+

[3]

Evertse JH, 2002, INT MATH RES NOTICES, V2002, P1295

[4]

Hodge, 1952, METHODS ALGEBRAIC GE, VII

[5] AN EFFECTIVE SCHMIDT'S SUBSPACE THEOREM FOR HYPERSURFACES IN SUBGENERAL POSITION IN PROJECTIVE VARIETIES OVER FUNCTION FIELDS [J].

Le, Giang .

KODAI MATHEMATICAL JOURNAL, 2018, 41 (01) :52-69

[6] SOMETIMES EFFECTIVE "THUE-SIEGEL-ROTH-SCHMIDT-NEVANLINNA BOUNDS, OR BETTER [J].

OSGOOD, CF .

JOURNAL OF NUMBER THEORY, 1985, 21 (03) :347-389

[7]

Osgood CF., 1981, INDIAN J MATH, V23, P1

[8]

Quang, 2022, J GEOM ANAL, V32

[9] An Effective Schmidt's Subspace Theorem for Projective Varieties Over Function Fields [J].

Ru, Min ;

Wang, Julie Tzu-Yueh .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2012, 2012 (03) :651-684

[10] Holomorphic curves into algebraic varieties [J].

Ru, Min .

ANNALS OF MATHEMATICS, 2009, 169 (01) :255-267

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