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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 | |