Reconstruction of a Variety from the Derived Category and Groups of Autoequivalences
We consider smooth algebraic varieties with ample either canonical or anticanonical sheaf. We prove that such a variety is uniquely determined by its derived category of coherent sheaves. We also calculate the group of exact autoequivalences for these categories. The technics of ample sequences in Abelian categories is used.
Key Words: derived categories; coherent sheaves; autoequivalences; Serre functor.