Reconstruction of a variety from the derived category and groups of autoequivalences

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.

arXiv comment20 pages, AMS-LaTeX file, this is an extended version of the chapter 4 of our paper alg-geom//9506012

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