代数几何方法(第3卷)

《代数几何方法》共三卷，本书是第三卷，共分三章。本书主要讨论了变分的算术理论和双元几何的基础。第一章介绍了与代数簇有关的基本概念（不可约性、相对性和绝对性、维数、一般点等），并详细阐述了簇的相关形式的性质；第二章给出了代数对应的一般理论；最后一章介绍了簇上圈的等价理论，并证明了Segre簇的基的存在性。本系列图书由浅入深，给出了作者对掌握代数几何方法知识的独到见解，为深入掌握经典几何的理论奠定了良好的代数基础。本书适合高等院校师生、相关专业的爱好者及研究者参考阅读。

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