Derived categories and birationality
arXiv:2001.05995
Abstract
We discuss the question of finding conditions on a derived equivalence between two smooth projective varieties and that imply that and are birational. The types of conditions we consider are in the spirit of finding categorical analogous of classical Torelli theorems. We study, in particular, a notion of strongly filtered derived equivalence and study cases where strongly filtered derived equivalence implies birationality. We also consider an open variant of our main question.
Paper is withdrawn in order to break it into more manageable parts. In addition, Theorem 3.2 is false as stated. A fixed version of the relevant material is now found at arXiv:2208.14378