%0 Generic %1 floccari2019mumfordtate %A Floccari, Salvatore %D 2019 %K Hyperkähler %T On the Mumford-Tate conjecture for hyperkähler varieties %U http://arxiv.org/abs/1904.06238 %X 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.

@misc{floccari2019mumfordtate, abstract = {We study the Mumford-Tate conjecture for hyperk\"{a}hler 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 hyperk\"{a}hler 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 Andr\'{e}.}, added-at = {2019-04-15T13:52:27.000+0200}, author = {Floccari, Salvatore}, biburl = {https://www.bibsonomy.org/bibtex/20ae5afe14f8ae5292beccceebcf976ed/simonechiarello}, description = {On the Mumford-Tate conjecture for hyperk\"{a}hler varieties}, interhash = {c6d85c1d3d84da93922b1ffe15966486}, intrahash = {0ae5afe14f8ae5292beccceebcf976ed}, keywords = {Hyperkähler}, note = {cite arxiv:1904.06238Comment: 16 pages}, timestamp = {2019-04-15T13:52:27.000+0200}, title = {On the Mumford-Tate conjecture for hyperk\"{a}hler varieties}, url = {http://arxiv.org/abs/1904.06238}, year = 2019 }