Daniel Huybrechts completed his Ph.D. in 1992 at the Universität Berlin. He is now a professor at the Institut de Mathématiques de Jussieu, Université Paris VII.

• 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

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.

Daniel Huybrechts completed his Ph.D. in 1992 at the Universität Berlin. He is now a professor at the Institut de Mathématiques de Jussieu, Université Paris VII.

• 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

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.

Daniel Huybrechts completed his Ph.D. in 1992 at the Universität Berlin. He is now a professor at the Institut de Mathématiques de Jussieu, Université Paris VII.

• 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

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.