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

Published online by Cambridge University Press:  04 December 2007

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

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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.

Keywords

derived categoriescoherent sheavesautoequivalencesSerre functor
Type
Research Article
Information
Compositio Mathematica , Volume 125 , Issue 3 , February 2001 , pp. 327 - 344
Copyright
© 2001 Kluwer Academic Publishers