Toward a Numerical Theory of Ampleness

Introduction Chapter I. Intersection Numbers ? 1. The polynomial theorem of Snapper ? 2. The definition and some properties of intersection numbers ? 3. Degrees and Hilbert polynomials ? 4. Numerically effective and numerically trivial invertible sheaves Chapter II. Some Vanishing Theorems and Related Results ? 1. M-families ?2. Some vanishing theorems and related results Chapter III. Ampleness and Pseudoampleness ? 1. The numerical characterization of ampleness ? 2. Pseudoampleness Chapter IV. The Ample Cone ? 1. The vector space A'(V) ? 2. The ample cone ? 3. Polarization ? 4. Relativization ? 5. The characteristic cone of a proper morphism Bibliography