I would like to know how derived categories (in particular, derived categories of coherent sheaves) can give results about "Traditional Algebraic Geometry". I am mostly interested in classical problems. For example: moduli spaces problems, automorphism groups of varieties, birational classification of varieties, minimal model program and so on.


Furthermore, I would also be interested to know about theorems that are more aesthetically pleasing being stated in the derived category language. For instance, I think Serre duality can be generalised to singular varieties through derived categories.


Any reference about results is very welcome.



Applications of derived categories to "Traditional Algebraic Geometry"
I think that a good example of the usefulness of the Derived Category of coherent sheaves for studying classical questions is the recent preprint by Soheyla Feyzbakhsh 


[Mukai's program (reconstructing a K3 surface from a curve) via wall-crossing](https://arxiv.org/abs/1710.06692),


where the author uses wall-crossing with respect to Bridgeland stability conditions in order to solve the classical Mukai problem of reconstructing a K3 surface from its hyperplane section.


