Deformation principle and André motives of projective hyperkähler manifolds

2019/04/25 by Soldatenkov, Andrey
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.11320

Abstract

Let X₁ and X₂ be deformation equivalent projective hyperkähler manifolds. We prove that the André motive of X₁ is abelian if and only if the André motive of X₂ is abelian. Applying this to manifolds of K3^[n], generalized Kummer and OG6 deformation types, we deduce that their André motives are abelian. As a consequence, we prove that all Hodge classes in arbitrary degree on such manifolds are absolute. We discuss applications to the Mumford-Tate conjecture, showing in particular that it holds for even degree cohomology of such manifolds.

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