Fourier-Mukai on K3 surfaces

  • Claudio BartocciEmail author
  • Ugo Bruzzo
  • Daniel Hernández Ruipérez
Part of the Progress in Mathematics book series (PM, volume 276)


In looking for examples of Fourier-Mukai transforms on varieties other than the Abelian ones, it is natural to consider K3 surfaces, especially in view of Theorem 2.38 and the subsequent discussion.

A forerunner of a Fourier-Mukai functor for K3 surfaces (which in our notation is a morphism of the type f Q: H •(X; Z) → H•(Y,Z), cf. Eq. (1.12)) was introduced by Mukai in [227]. When trying to define a Fourier-Mukai functor in the proper sense, one realizes that it is necessary to limit the class of K3 surfaces one considers; essentially one needs to require that the Picard lattice contains some preferred sublattice. A first example was given in [24] where a class of K3 surfaces called (strongly) reexive was introduced. Another example by Mukai appeared later [228].


Modulus Space Exact Sequence Line Bundle Hilbert Scheme Coherent Sheaf 
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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  • Claudio Bartocci
    • 1
    Email author
  • Ugo Bruzzo
    • 2
  • Daniel Hernández Ruipérez
    • 3
  1. 1.Dipartimento di MatematicaUniversità di GenovaGenovaItaly
  2. 2.Scuola Internazionale Superiore di Studi Avanzati and Istituto Nazionale di Fisica NucleareTriesteItaly
  3. 3.Departamento de Matemáticas and Instituto Universitario de Fisica Fundamental y MatemáticasUniversidad de SalamancaSalamancaSpain

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