In English phrases like 

> 
> Jesse is a friend **of mine**/**\*of me**
> 
> 
> 

the case of the word "mine" is not the oblique ("me") which usually occurs with prepositions ("That's a part **of me** that you don't see too often")

What licenses the genitive case ("my/mine") in possessional phrases with the preposition "of" instead of the oblique case ("me"), which most prepositional phrases take?

A few more examples (where the # ones sound a bit odd to me, but that just might be semantic satiation messing with my judgements):

> 
> I am a friend **of Jesse's**/#**of Jesse**
> 
> 
> I like that girlfriend **of Jesse's**/#**of Jesse**
> 
> 
> I'm a friend **of the king**/#**of the king's**
> 
> 
> She has the voice **of an angel**/**\*of an angel's**
> 
> 
>