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| Triangulated categories | |
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| Additive categories and functors | |
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| Triangulated categories and exact functors | |
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| Equivalences of triangulated categories | |
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| Exceptional sequences and orthogonal decompositions | |
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| Derived categories: a quick tour | |
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| Derived category of an abelian category | |
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| Derived functors | |
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| Spectral sequences | |
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| Derived categories of coherent sheaves | |
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| Basic structure | |
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| Spanning classes in the derived category | |
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| Derived functors in algebraic geometry | |
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| Grothendieck-Verdier duality | |
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| Derived category and canonical bundle - I | |
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| Ample (anti-)canonical bundle | |
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| Autoequivalences for ample (anti-)canonical bundle | |
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| Ample sequences in derived categories | |
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| Fourier-Mukai transforms | |
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| What it is and Orlov's result | |
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| Passage to cohomology | |
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| Derived category and canonical bundle - II | |
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| Kodaira dimension under derived equivalence | |
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| Geometrical aspects of the Fourier-Mukai kernel | |
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| Nefness under derived equivalence | |
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| Derived equivalence versus birationality | |
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| Recap: Kodaira dimension, canonical ring, etc. | |
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| Equivalence criteria for Fourier-Mukai transforms | |
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| Fully faithful | |
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| Equivalences | |
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| Canonical quotients | |
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| Spherical and exceptional objects | |
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| Autoequivalences induced by spherical objects | |
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| Braid group actions | |
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| Beilinson spectral sequence | |
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| They go together | |
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| Abelian varieties | |
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| Basic definitions and facts | |
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| The Poincare bundle as a Fourier-Mukai kernel | |
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| Sl[subscript 2]-action | |
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| Derived equivalences of abelian varieties | |
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| Autoequivalences of abelian varieties | |
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| K3 surfaces | |
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| Recap: K3 surfaces | |
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| Derived equivalence of K3 surfaces | |
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| Recap: Moduli spaces of sheaves | |
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| Flips and flops | |
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| Preparations: Closed embeddings and blow-ups | |
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| Derived categories under blow-up | |
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| The standard flip | |
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| The Mukai flop | |
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| Derived categories of surfaces | |
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| Recap: Enriques classification of algebraic surfaces | |
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| Minimal surfaces with kod = -[infinity], 2 | |
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| Surfaces with torsion canonical bundle | |
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| Properly elliptic surfaces | |
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| Where to go from here | |
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| McKay correspondence for derived categories | |
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| Homological mirror symmetry | |
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| D-branes and stability conditions | |
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| Twisted derived categories | |
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| References | |
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| Index | |