Given a K3 surface, M. Kuga and I. Satake  associate to it an abelian variety. P. Deligne  has constructed an absolute Hodge cycle on the product of the abelian variety and the K3 surface. When the K3 surface is the desingularisation of a double cover of the plane branched along six lines in general position, the abelian variety is isogenous to the product of a number of copies of a four dimensional abelian variety. We construct the Kuga-Satake-Deligne correspondence between this four dimensional abelian variety and the K3 surface in this case.
More precisely, we prove
Theorem 2.1. Let Y 1 be the desingularisation of the double cover of the plane branched along six lines in general position. Then there is an abelian variety P and a codimension two algebraic cycle on P × Y 1 such that the homomorphism
is an inclusion when restricted to the lattice of transcendental cycles of Y 1, and hence this cycle represents the Kuga-Satake-Deligne correspondence.
This result settles affirmatively a special case of the Hodge conjecture.