Thanks for joining the NUC community.
The maximum supported resolution is 3840 x 2160 @ 30 Hz, 24bpp, this is via Display Port.
Here is the information about 4k: http://downloadmirror.intel.com/23090/eng/D54250WYB_D34010WYB_TechProdSpec06.pdf
Please bear in mind that Intel does not test and validate Intel® NUC on Linux, however we know that a lot of NUC owners are using it successfully on many different Linux distros. Intel suggests you check your Linux distro's website and forums at linux.com for peer assistance with this issue.