# On the Mumford–Tate conjecture for hyperkähler varieties

@article{Floccari2019OnTM,
title={On the Mumford–Tate conjecture for hyperk{\"a}hler varieties},
author={Salvatore Floccari},
journal={arXiv: Algebraic Geometry},
year={2019}
}
We study the Mumford-Tate conjecture for hyperkahler varieties. Building on work of Markman, we show that it holds in arbitrary codimension for all varieties of $\mathrm{K}3^{[m]}$-type. For an arbitrary hyperkahler 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 Andre.
2 Citations
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