Hi Leonard, I checked out your file, and yes it does just seem to be not illuminated well... 
Note that the edge that you are talking about is angled downward somewhat like this:
  
So that means that a light shining from directly above it will not illuminate it, it is hidden from that light.
 
The main one that could possibly illuminate it would be this light over here:
  
That's light#4, but you seem to have disabled it so that it does not do anything in the renderer currently, note that "Visible in Renderer" for that light is set to Off:
  
You'll need to enable that light and possibly adjust the overall lighting some more to make that edge not be so dark.
 
As far as I can tell your model data is all perfect, you just need to shine some light on that area if you don't want it to be dark.
 
    - Michael  
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