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

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

1997-12-24

arxiv.org/abs/alg-geom/9712029v1

Compositio Math. 125 (2001), no. 3, 327--344

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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