判别式结式和多维行列式

Preface

Introduction

I. GENERAL DISCRIMINANTS AND RESULTANTS

CHAPTER I. Projective Dual Varieties and GeneralDiscriminants

I. Definitions and basic examples

2. Duality for plane curves

3. The incidence variety and the proof of the bidualitytheorem

4. Further examples and properties of projective duality

5. The Katz dimension formula and its applications

CHAPTER 2. The Cayley Method for Studying Discriminants

1. Jet bundles and Koszul complexes

2, Discriminantai complexes

3, The degree and the dimension of the dual

4. Discriminantal complexes in terms of differential forms

5. The discriminant as the determinant of a spectral sequence

CHAPTER 3. Associated Varieties and General Resultants

1. Grassmannians. Preliminary material

2. Associated hypersurfaces

3. Mixed resultants

4. The Cayley method for the study of resultants

CHAPTER 4. Chow Varieties

1. Definitions and main properties

2. 0-cycles, factorizable forms and symmetric products

3. Cayley-Green-Morrison equations of Chow varieties

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This book has expanded from our attempt to construct a general iheory of hyper-geometric functions and can be regarded as a first step towards its systematic exposition. However， this step turned out to be so interesting and important， and the whole program so overwhelming， that we decided to present it as a separate work. Moreover， in the process of writing we discovered a beautiful area which had been nearly forgotten so that our work can be regarded as a natural continuation of the classical developments in algebra during the 19th century.