Andrey Soldatenkov

Andrey Soldatenkov
Humboldt-Universität zu Berlin | HU Berlin · Department of Mathematics

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7
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Publications

Publications (7)
Article
Let $X_1$ and $X_2$ be deformation equivalent projective hyperkähler manifolds. We prove that the André motive of $X_1$ is abelian if and only if the André motive of $X_2$ is abelian. Applying this to manifolds of $\mbox {K3}^{[n]}$, generalized Kummer and OG6 deformation types, we deduce that their André motives are abelian. As a consequence, we p...
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The purpose of this note is to give an account of a well-known folklore result: the Hodge structure on the second cohomology of a compact hyperk\"ahler manifold uniquely determines Hodge structures on all higher cohomology groups. We discuss the precise statement and its proof, which are somewhat difficult to locate in the literature.
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We study Andr\'e motives of projective hyperk\"ahler manifolds that are deformation equivalent to the generalized Kummer varieties. We prove that the motives of such manifolds are abelian, i.e. they are contained in the subcategory generated by the motives of abelian varieties. As a consequence, we prove that all Hodge classes in arbitrary degree o...
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This note is inspired by the work of Deligne on the local behavior of Hodge structures at infinity. We study limit mixed Hodge structures of degenerating families of compact hyperk\"ahler manifolds. We show that when the monodromy action on $H^2$ has maximal index of unipotency, the limit mixed Hodge structures on all cohomology groups are of Hodge...
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We extend the Kuga-Satake construction to the case of limit mixed Hodge structures of K3 type. We use this to study the geometry and Hodge theory of degenerations of Kuga-Satake abelian varieties, associated to polarized variations of K3 type Hodge structures over the punctured disc.