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Fourier-Mukai Transforms in Algebraic Geometry$
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D. Huybrechts

Print publication date: 2006

Print ISBN-13: 9780199296866

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199296866.001.0001

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Derived Category and Canonical Bundle – I

Derived Category and Canonical Bundle – I

(p.90) 4 Derived Category and Canonical Bundle – I
Fourier-Mukai Transforms in Algebraic Geometry

D. Huybrechts

Oxford University Press

This chapter is devoted to results by Bondal and Orlov which show that for varieties with ample (anti-)canonical bundle, the bounded derived category of coherent sheaves determines the variety. Except for the case of elliptic curves, this settles completely the classification of derived categories of smooth curves. The complexity of the derived category is reflected by its group of autoequivalences. This is studied by means of ample sequences.

Keywords:   ample canonical bundle, curves, autoequivalences, ample sequences

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