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On the Mumford-Tate conjecture for hyperkähler varieties

. (2019)cite arxiv:1904.06238Comment: 16 pages.

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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On the Mumford-Tate conjecture for hyperk\"{a}hler varieties

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