Deformation principle and Andr\'e motives of projective hyperk\'ahler manifolds
| Autor: | Soldatenkov, Andrey |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $X_1$ and $X_2$ be deformation equivalent projective hyperk\"ahler manifolds. We prove that the Andr\'e motive of $X_1$ is abelian if and only if the Andr\'e motive of $X_2$ is abelian. Applying this to manifolds of $\mbox{K3}^{[n]}$, generalized Kummer and OG6 deformation types, we deduce that their Andr\'e 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. Comment: 20 pages, expanded sections 5 and 6; to appear in IMRN |
| Databáze: | arXiv |
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