《Geometry of Aggregates》

INTRODUCTION1

PREPARATION7

1．The projective r-dimensional space Sr7

2．The dual space8

3．Subspaces of Sr;Substars of r9

4．Algebraic manifolds11

5．Projections14

6．Birational correspondences14

CHAPTER Ⅰ －SEGRE MANIFOLDS16

1．The twofold projective space16

2．The manifold[m;n]h19

3．The prime-manifold]m;n[h26

4．Correlations30

CHAPTER Ⅱ －PROJECTIVELY GENERATED MANIFOLDS IN ARBITRARY SPACES36

1．Projectively generated manifolds in a space of arbitrary dimension36

2．Submanifolds ofSr40

3．Pairing Theorems and Double-N Theorem44

4．Aggregates48

CHAPTER Ⅲ －BIRATIONAL CORRESPONDENCES52

1．The birationally related manifoldsSr and Sm52

2．Representation of Sr and Sm by [m;r]0 SN-n-157

3．Apolar systems of aggregates61

CHAPTER Ⅳ －PENCILS OF TWO-DIMENSIONAL AGGREGAEST IN THREE-SPACE65

1．The linear system of 1 two-dimensional contravariant aggregates in S365

2．The relation between the manifoldsS3 and S266

3．A representation of S3 in the matrix-space S1168

4．Representation of S2 in the matrix-space S1171

5．Particular systems of aggregates ]l|2[0 S373

CHAPTER Ⅴ －NETS OF TWO-DIMENSIONAL AGGREGATES IN THREE-SPACE78

1．The linear system of 2 two-dimensional contravariant aggregates in S378

2．The relation between the manifoldsS3 and S279

3．The representation of S3 in the matrix-space S1183

4．The representation of S2 in the matrix-space S1185

5．Particular systems of aggregates ]2|2[0 S387

CHAPTER Ⅵ －A SURVEY OF FURTHER DEVELOPMENTS93

1．The system of aggregates ]3|2[0S393

2．The system of aggregates ]4|2[0 S394

REFERENCES96

INDEX98