The Kuga-Satake variety of an abelian surface

Abelian Varieties of Weil Type and Kuga-satake Varieties

We analyze the relationship between abelian fourfolds of Weil type and Hodge structures of type K3, and we extend some of these correspondences to the case of arbitrary dimension.

Kuga-satake Varieties and the Hodge Conjecture

Kuga-Satake varieties are abelian varieties associated to certain weight two Hodge structures, for example the second cohomology group of a K3 surface. We start with an introduction to Hodge structures and we give a detailed account of the construction of Kuga-Satake varieties. The Hodge conjecture is discussed in section 2. An excellent survey of the Hodge conjecture for abelian varieties is [...

A generalization of the Kuga-Satake construction

The Kuga-Satake construction [3] associates to a polarized Hodge structure H of weight 2 with h2,0 = 1 an abelian variety A which satisfies the property that H is a sub-Hodge structure of Hom (H1(A),H1(A)). The construction is very tricky and intriguing geometrically: one first associates to the lattice (H,<,>) its Clifford algebra C(H), which is again a lattice. Then one constructs a complex s...

Real multiplication on K3 surfaces and Kuga Satake varieties

The endomorphism algebra of a K3 type Hodge structure is a totally real field or a CM field. In this paper we give a low brow introduction to the case of a totally real field. We give existence results for the Hodge structures, for their polarizations and for certain K3 surfaces. We consider the Kuga Satake variety of these Hodge structures and we discuss some examples. Finally we indicate vari...

On the Quotient Variety of an Abelian Variety.