作者：(以)罗恩·佩雷茨(Ronen Pere
页数：203页
出版社：哈尔滨工业大学出版社
出版日期：2022
ISBN：9787560399416
电子书格式：pdf/epub/txt
内容简介
本书描述了解决2维问题的一个方法。从代数观点来看，本书考虑了2维多项式代数的子代数，该子代数是由参数化这些奇异曲面的多项式产生的。分为19章，具体内容包括：多项式映射的渐近值和序列渐近值、雅可比猜想的结式公式化、根据导数给代数分次、雅可比对的结式的基本属性、可逆态射及其结果和逆公式、用格拉斯曼多项式表达雅可比(行列式)和结式等。
目录
1 introduction
2 A Theorem of J. Hadamard
3 Asymptotic and Sequential Asymptotic Values of Polynomial Maps
4 The Asymptotic Values of a Polynomial Map C2 → C2 Form a Va-riety which is the Union of Two Natural Algebraic Curves in C2
5 The Resultant Formulation of the Jacobian Conjecture
6 The Jacobian Conjecture in Dimension 2 is Decidable
7 A Straight Forward Inductive Approach Fails
8 Grading an Algebra with a Derivation – Introduction
9 Grading an Algebra According To a Derivation
10 The Structure of the D-classes
11 Application to Automorphisms of Polynomial Rings
12 Elementary Properties of Resultants of Jacobian Pairs
13 Invertible Morphisms their Resultants and Inversion Formulas
14 The Rigidity of Morphisms
15 The Fibre Theorem
16 Expressing the Jacobian and the Resultant in Grassmann Coordi-nates
17 One More Inversion Formula and an Equivalent Formulation to the Jacobian Conjecture
18 Parametrization of the Jacobian Variety
19 More Statements which are Equivalent to the Jacobian Conjecture
Bibliography
编辑手记
2 A Theorem of J. Hadamard
3 Asymptotic and Sequential Asymptotic Values of Polynomial Maps
4 The Asymptotic Values of a Polynomial Map C2 → C2 Form a Va-riety which is the Union of Two Natural Algebraic Curves in C2
5 The Resultant Formulation of the Jacobian Conjecture
6 The Jacobian Conjecture in Dimension 2 is Decidable
7 A Straight Forward Inductive Approach Fails
8 Grading an Algebra with a Derivation – Introduction
9 Grading an Algebra According To a Derivation
10 The Structure of the D-classes
11 Application to Automorphisms of Polynomial Rings
12 Elementary Properties of Resultants of Jacobian Pairs
13 Invertible Morphisms their Resultants and Inversion Formulas
14 The Rigidity of Morphisms
15 The Fibre Theorem
16 Expressing the Jacobian and the Resultant in Grassmann Coordi-nates
17 One More Inversion Formula and an Equivalent Formulation to the Jacobian Conjecture
18 Parametrization of the Jacobian Variety
19 More Statements which are Equivalent to the Jacobian Conjecture
Bibliography
编辑手记
