Claire Voisin
Published 2005-03-07Version 1
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.
Tate twists of Hodge structures arising from abelian varieties of type IV
Hodge structures on abelian varieties of type III
Rational curves on quotients of abelian varieties by finite groups
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