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Mathematische Zeitschrift

, Volume 272, Issue 1–2, pp 577–588 | Cite as

Non-uniqueness of Fourier–Mukai kernels

  • Alberto Canonaco
  • Paolo StellariEmail author
Article

Abstract

We prove that the kernels of Fourier–Mukai functors are not unique in general. On the other hand we show that the cohomology sheaves of those kernels are unique. We also discuss several properties of the functor sending an object in the derived category of the product of two smooth projective schemes to the corresponding Fourier–Mukai functor.

Keywords

Derived categories Fourier–Mukai functors 

Mathematics Subject Classification (2000)

14F05 18E25 18E30 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica “F. Casorati”Università degli Studi di PaviaPaviaItaly
  2. 2.Dipartimento di Matematica “F. Enriques”Università degli Studi di MilanoMilanItaly

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