On the Mumford-Tate conjecture for hyperkähler varieties
arXiv:1904.06238 · doi:10.1007/s00229-021-01316-4
Abstract
We study the Mumford--Tate conjecture for hyperkähler varieties. We show that the full conjecture holds for all varieties deformation equivalent to either an Hilbert scheme of points on a K3 surface or to O'Grady's ten dimensional example, and all of their self-products. For an arbitrary hyperkähler variety whose second Betti number is not 3, we prove the Mumford--Tate conjecture in every codimension under the assumption that the Künneth components in even degree of its André motive are abelian. Our results extend a theorem of André.
final version, to appear in Manuscripta Mathematica