English

Derived categories and birationality

Algebraic Geometry 2022-09-02 v3

Abstract

We discuss the question of finding conditions on a derived equivalence between two smooth projective varieties XX and YY that imply that XX and YY 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.

Keywords

Cite

@article{arxiv.2001.05995,
  title  = {Derived categories and birationality},
  author = {Max Lieblich and Martin Olsson},
  journal= {arXiv preprint arXiv:2001.05995},
  year   = {2022}
}

Comments

Paper is withdrawn in order to break it into more manageable parts.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

R2 v1 2026-06-23T13:13:20.355Z