Abstract
We study the Mumford-Tate conjecture for hyperkähler varieties. Building
on work of Markman, we show that it holds in arbitrary codimension for all
varieties of $K3^m$-type. For an arbitrary hyperkähler variety
satisfying $b_2(X)>3$ we establish one of the two inclusions of algebraic
groups predicted by the Mumford-Tate conjecture. Our results extend a theorem
of André.
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