Depending on how much the skill is leveled up,

it turns out that the Lich Crown adds to Dark Magic; I didn't pay attention.
Now I checked: when the skill is leveled up to 19, it adds +9, for a total of 28 – you can deal some serious damage :D

Basically, the crown is the same as the staff, only for Dark Magic; the bonuses are equivalent. The rings have the exact same effect. It's a pity that the effect from two items doesn't stack, just like with other skills.