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Non-uniqueness of Fourier–Mukai kernels

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica “F. Casorati”, Università degli Studi di Pavia, Via Ferrata 1, 27100, Pavia, Italy

    Alberto Canonaco

  2. Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Cesare Saldini 50, 20133, Milan, Italy

    Paolo Stellari

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  1. Alberto Canonaco
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  2. Paolo Stellari
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Correspondence to Paolo Stellari.

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Canonaco, A., Stellari, P. Non-uniqueness of Fourier–Mukai kernels. Math. Z. 272, 577–588 (2012). https://doi.org/10.1007/s00209-011-0950-3

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  • DOI: https://doi.org/10.1007/s00209-011-0950-3

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