作者：(英)W. V. D.霍奇(W. V.
页数：394页
出版社：哈尔滨工业大学出版社
出版日期：2021
ISBN：9787560394299
电子书格式：pdf/epub/txt
内容简介
本书是一套版权引进的数学专著丛书的第3卷，本卷书的写作目的是说明可用于研究代数簇的双有理几何的现代代数方法。
目录
PREFACE
BIRATIONAL GEOMETRY
CHAPTER XV: IDEAL THEORY OF COMMUTATIVE RINGS
1. Ideals in a commutative ring
2. Prime ideals and primary ideals
3. Remainder-class rings
4. Subrings and extension rings
5. Quotient rings
6. Modules
7. Multiplieative theory of ideals
8. Integral dependence
CHAPTER XVI: THE ARITHMETIC THEORY OF VARIETIES
1. Algebraic varieties in affine space
2. Ideals and varieties in affine space
3. Simple points
4. Irreducible subvarieties of Vd
5. Normal varieties in affine space
6. Proj ectively normal varieties
CHAPTER XVII: VALUATION THEORY
1. Ordered Abelian groups
2. Valuations of a field
3. Residue fields
4. Valuations of algebraic function fields
5. The centre of a valuation
CHAPTER XVIII: BIRATIONAL TRANSFORMATIONS
1. Birational correspond ences
2. Birational correspond ences between normal varieties
3. Monoidal transformations
4. The reduction of singularities and the Local Uniformisation Theorem
5. Some Cremona transformations
6. The Local Uniformisation Theorem : the main CaSe
7. Valuations of dimensions and rank k
8. Resolving systems
9. The reduction of the singularities of an algebraic variety
BIBLIOGRAPHICAL NOTES
BIBLIOGRAPHY
INDEX
编辑手记
BIRATIONAL GEOMETRY
CHAPTER XV: IDEAL THEORY OF COMMUTATIVE RINGS
1. Ideals in a commutative ring
2. Prime ideals and primary ideals
3. Remainder-class rings
4. Subrings and extension rings
5. Quotient rings
6. Modules
7. Multiplieative theory of ideals
8. Integral dependence
CHAPTER XVI: THE ARITHMETIC THEORY OF VARIETIES
1. Algebraic varieties in affine space
2. Ideals and varieties in affine space
3. Simple points
4. Irreducible subvarieties of Vd
5. Normal varieties in affine space
6. Proj ectively normal varieties
CHAPTER XVII: VALUATION THEORY
1. Ordered Abelian groups
2. Valuations of a field
3. Residue fields
4. Valuations of algebraic function fields
5. The centre of a valuation
CHAPTER XVIII: BIRATIONAL TRANSFORMATIONS
1. Birational correspond ences
2. Birational correspond ences between normal varieties
3. Monoidal transformations
4. The reduction of singularities and the Local Uniformisation Theorem
5. Some Cremona transformations
6. The Local Uniformisation Theorem : the main CaSe
7. Valuations of dimensions and rank k
8. Resolving systems
9. The reduction of the singularities of an algebraic variety
BIBLIOGRAPHICAL NOTES
BIBLIOGRAPHY
INDEX
编辑手记
