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