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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 Categories of Surfaces

Derived Categories of Surfaces

(p.272) 12 Derived Categories of Surfaces
Fourier-Mukai Transforms in Algebraic Geometry

D. Huybrechts

Oxford University Press

This chapter completes the classification of algebraic surfaces from the point of view of their derived categories. Abelian, K3, and elliptic surfaces play a special role. For all other surfaces, the derived category determines the isomorphism type. The reduction to minimal surfaces is due to Kawamata, and the case of elliptic surfaces was dealt with by Bridgeland and Maciocia.

Keywords:   abelian surfaces, K3 surfaces, elliptic surfaces, minimal surfaces, Enriques classification

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