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Fourier-Mukai Transforms in Algebraic Geometry
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Table of Contents

Preface ; 1. Triangulated categories ; 2. Derived categories: a quick tour ; 3. Derived categories of coherent sheaves ; 4. Derived category and canonical bundle I ; 5. Fourier-Mukai transforms ; 6. Derived category and canonical bundle II ; 7. Equivalence criteria for Fourier-Mukai transforms ; 8. Spherical and exceptional objects ; 9. Abelian varieties ; 10. K3 surfaces ; 11. Flips and flops ; 12. Derived categories of surfaces ; 13. Where to go from here ; References ; Index

About the Author

Daniel Huybrechts completed his Ph.D. in 1992 at the Universitat Berlin. He is now a professor at the Institut de Mathematiques de Jussieu, Universite Paris VII.

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It is a very good starting point to explore open problems related to derived categories, such as for example moduli space problems and birational classification. * Marcello Bernardara, Zentralblatt MATH Vol 1095 *

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