A generalization of the Kuga-Satake construction

Details A generalization of the Kuga-Satake construction A generalization of the Kuga-Satake construction

2005-03-07

arxiv.org/abs/math/0503122v1

Mathematics

Algebraic Geometry

Scientific paper

The Kuga-Satake construction associates to a K3 type polarized weight 2 Hodge structure H an abelian variety A such that H is a quotient Hodge structure of H^2(A). The first step is to consider the Clifford algebra of H. It turns out that it is endowed with a weight 2 Hodge structure compatible with the algebra structure. We show more generally that a weight 2 polarized Hodge structure which carries a compatible (unitary, associative) algebra structure is a quotient of the H^2 of an abelian variety.

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