# Fourier-Mukai on K3 surfaces

## 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## Preview

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