Geometry of AggregatesPDF电子书下载

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INTRODUCTION 1

PREPARATION 7

1．The projective r-dimensional space Sr 7

2．The dual space 8

3．Subspaces of Sr;Substars of r 9

4．Algebraic manifolds 11

5．Projections 14

6．Birational correspondences 14

CHAPTER Ⅰ －SEGRE MANIFOLDS 16

1．The twofold projective space 16

2．The manifold[m;n]h 19

3．The prime-manifold]m;n[h 26

4．Correlations 30

CHAPTER Ⅱ －PROJECTIVELY GENERATED MANIFOLDS IN ARBITRARY SPACES 36

1．Projectively generated manifolds in a space of arbitrary dimension 36

2．Submanifolds of Sr 40

3．Pairing Theorems and Double-N Theorem 44

4．Aggregates 48

CHAPTER Ⅲ －BIRATIONAL CORRESPONDENCES 52

1．The birationally related manifolds Sr and Sm 52

2．Representation of Sr and Sm by [m;r]0 SN-n-1 57

3．Apolar systems of aggregates 61

CHAPTER Ⅳ －PENCILS OF TWO-DIMENSIONAL AGGREGAEST IN THREE-SPACE 65

1．The linear system of 1 two-dimensional contravariant aggregates in S3 65

2．The relation between the manifolds S3 and S2 66

3．A representation of S3 in the matrix-space S11 68

4．Representation of S2 in the matrix-space S11 71

5．Particular systems of aggregates ]l|2[0 S3 73

CHAPTER Ⅴ －NETS OF TWO-DIMENSIONAL AGGREGATES IN THREE-SPACE 78

1．The linear system of 2 two-dimensional contravariant aggregates in S3 78

2．The relation between the manifolds S3 and S2 79

3．The representation of S3 in the matrix-space S11 83

4．The representation of S2 in the matrix-space S11 85

5．Particular systems of aggregates ]2|2[0 S3 87

CHAPTER Ⅵ －A SURVEY OF FURTHER DEVELOPMENTS 93

1．The system of aggregates ]3|2[0 S3 93

2．The system of aggregates ]4|2[0 S3 94

REFERENCES 96

INDEX 98

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