●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. ltiplieative 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
編輯手記

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