●PREFACE
BOOK III GENERAL THEORY OF ALGEBRAIC VARIETIES IN PROJECTIVE SPACE
CHAAPTER X: ALGEBRAIC VARIETIES
1.Introduction
2.Reducible and irreducible varieties
3.Generic points of an irreducible variety
4.Generic members of systems of k-spaces
5.The dimension of an algebraic variety
6.The Cayley form of an algebraic variety
7.Properties of the Cayley form
8.Further properties of the Cayley form
9.The order of an algebraic variety; parametrisation
10.Some algebraic lemmas
11.Absolutely and relatively irreducible varieties
12.Some properties of relatively irreducible varieties
13.Sections of an absolutely irreducible variety
14.Tangent spaces and simple points
CHAPTER XI: ALGEBRAIC CORRESPONDENCES
1.Varieties in r-way projective space
2.Segre's representation of r-way projective space
3.Two-way algebraic correspondences
4.The Principle of Counting Constants
5.A special correspondence
6.Systems of algebraic varieties and related correspondences
7.Normal problems
8. ltiplicative varieties
9.A criterion for unit multiplicity
10.Simple points
CHAPTER XII: INTERSECTION THEORY
1.Introduction
2.The degeneration of an irreducible variety in Sn
3.The product and cross.j oin of two irreducible varieties in Sn
4.The intersection of two irreducible varieties in Sn
5.Intersection theory in Sn
6.The intersection of irreducible varieties on a Vn in Sn
7.Intersection theory on a non-singular Vn
8.Intersections of systems of varieties
9.Equivalence on an algebraic variety
10.Virtual varieties
11.Theory of the base
BOOK IV QUADRICS AND GRASSMANN VARIETIES
CHAPTER XIII: QUADRICS
1.Definitions and elementary properties
2.Quadric primals in Sn
3.Polar theory of quadrics
4.Linear spaces on a quadric, I
5.Linear spaces on a quadric, II
6.The subvarieties of a quadric
7.Stereographic projection
8.The projective transfor- mations of a quadric into itself
9.The elementary divisors of orthogonal matrices
10.Pairs of quadrics
11.The intersection of two quadrics in Sn
CHAPTER XIV: GRASSMANN VARIETIES
1.Grassmann varieties
2.Schubert varieties
3.Equations of a Schubert variety
4.Intersections of Schubert varieties: point-set properties
5.The basis theorem
6.The intersection formulae
7.Applications to enumerative geometry
8.Varieties of dimension (n-d)(d+1)--I onΩ(d, n)
9. tulation formulae for
BIBLIOGRAPHICAL NOTES
BIBLIOGRAPHY
INDEX

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