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Equivalences of derived categories and K3 surfaces

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Abstract

We consider derived categories of coherent sheaves on smooth projective variaties. We prove that any equivalence between them can be represented by an object on the product. Using this, we give a necessary and sufficient condition for equivalence of derived categories of two K3 surfaces.

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Authors
  1. D. O. Orlov
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Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 41, Algebraic Geometry-7, 1997.

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Orlov, D.O. Equivalences of derived categories and K3 surfaces. J Math Sci 84, 1361–1381 (1997). https://doi.org/10.1007/BF02399195

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