21:9 2560x1080 on Mini late 2012 I just bought an LG 21:9 monitor, with a native resolution of 2560x1080p at 60 Hz.

Now, my mac mini late 2012 (HD4000) allow me to select resolutions up to 1920x1080p and no more. 
The monitor is connected via HDMI, but the HDMI on the mini should be able to output up to 2560x1440p@60Hz...

Any advice?
According to MacTracker.app:


Display Connection    1 - HDMI port or Thunderbolt digital video output
Display Support   Supports an HDMI-compatible device while using one Thunderbolt display or support for two Thunderbolt displays
Display Modes Dual display extended, video mirroring, and AirPlay Mirroring
External Resolution   Up to 2560 by 1600 (Thunderbolt) or 1920 by 1200 (HDMI)


Concluding: You need a Thunderbolt display adapter for your new display