Compositio Mathematica



Reconstruction of a Variety from the Derived Category and Groups of Autoequivalences


Alexei Bondal a1 and Dmitri Orlov a2
a1 Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia. E-mail: bondal@mi.ras.ru
a2 Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia. E-mail: orlov@mi.ras.ru

Article author query
bondal a   [Google Scholar] 
orlov d   [Google Scholar] 
 

Abstract

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.