English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

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 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.

Deformation Principle and André motives of Projective Hyperkähler Manifolds