A generalization of the Kuga-Satake construction
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0503122,
title = {A generalization of the Kuga-Satake construction},
author = {Claire Voisin},
journal= {arXiv preprint arXiv:math/0503122},
year = {2007}
}