Fully faithful functors, skyscraper sheaves, and birational equivalence

Chunyi Li, Xun Lin, Xiaolei Zhao

Let $X$ and $Y$ be two smooth projective varieties such that there is a fully faithful exact functor from $D^b(\mathrm{Coh}(X))$ to $D^b(\mathrm{Coh}(Y))$. We show that $X$ and $Y$…