Hi,
I used till now DVI to connect the PC to the monitor. I recently bought a
digitus 4K HDMI switch 4x1 to be able to switch between 3 HDMI inputs.
However when I switched on the PC and X started, all was messed.
Default resolution was 1280x720 instead 1920x1080. 
The display area is partially out of the monitor size, so that the panel is
not visible and lastly the quality of the image was really bad (like
insufficient frequency or sync or whatever)

I switched back to the DVI cable and I am wondering if someone can point me
to the right direction.

regards