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Fourier-Mukai on K3 surfaces

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

Abstract

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].

Keywords

Modulus Space Exact Sequence Line Bundle Hilbert Scheme Coherent Sheaf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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