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| Preface to the second edition | |
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| Preface to the first edition | |
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| Introduction | |
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| General Theory | |
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| Preliminaries | |
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| Some Homological Algebra | |
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| Semistable Sheaves | |
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| The Harder-Narasimhan Filtration | |
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| An Example | |
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| Jordan-H�lder Filtration and S-Equivalence | |
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| �-Semistability | |
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| Boundedness I | |
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| Families of Sheaves | |
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| Flat Families and Determinants | |
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| Grothendieck's Quot-Scheme | |
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| The Relative Harder-Narasimhan Filtration | |
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| Appendix | |
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| Flag-Schemes and Deformation Theory | |
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| A Result of Langton | |
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| Further comments (second edition) | |
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| The Grauert-M�lich Theorem | |
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| Statement and Proof | |
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| Finite Coverings and Tensor Products | |
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| Boundedness II | |
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| The Bogomolov Inequality | |
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| Appendix | |
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| e-Stability and Some Estimates | |
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| Further comments (second edition) | |
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| Moduli Spaces | |
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| The Moduli Functor | |
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| Group Actions | |
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| The Construction---Results | |
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| The Construction---Proofs | |
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| Local Properties and Dimension Estimates | |
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| Universal Families | |
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| Appendix | |
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| Gieseker's Construction | |
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| Decorated Sheaves | |
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| Change of Polarization | |
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| Further comments (second edition) | |
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| Sheaves on Surfaces | |
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| Construction Methods | |
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| The Serre Correspondence | |
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| Elementary Transformations | |
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| Examples of Moduli Spaces | |
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| Appendix | |
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| Further comments (second edition) | |
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| Moduli Spaces on K3 Surfaces | |
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| Low-Dimensional... | |
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| ...and Higher-Dimensional Moduli Spaces | |
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| Appendix | |
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| The Irreducibility of the Quot-scheme | |
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| Further comments (second edition) | |
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| Restriction of Sheaves to Curves | |
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| Flenner's Theorem | |
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| The Theorems of Mehta and Ramanathan | |
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| Bogomolov's Theorems | |
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| Appendix | |
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| Further comments (second edition) | |
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| Line Bundles on the Moduli Space | |
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| Construction of Determinant Line Bundles | |
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| A Moduli Space for �-Semistable Sheaves | |
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| The Canonical Class of the Moduli Space | |
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| Further comments (second edition) | |
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| Irreducibility and Smoothness | |
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| Preparations | |
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| The Boundary | |
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| Generic Smoothness | |
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| Irreducibility | |
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| Proof of Theorem 9.2.2 | |
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| Proof of Theorem 9.3.2 | |
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| Symplectic Structures | |
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| Trace Map, Atiyah Class and Kodaira-Spencer Map | |
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| The Tangent Bundle | |
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| Forms on the Moduli Space | |
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| Non-Degeneracy of Two-Forms | |
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| Appendix | |
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| Further comments (second edition) | |
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| Birational properties | |
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| Kodaira Dimension of Moduli Spaces | |
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| More Results | |
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| Examples | |
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| Appendix | |
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| Further comments (second edition) | |
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| References | |
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| Glossary of Notations | |
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| Index | |