I have experienced it in 303 Brit and 30-30Win, both being rimmed, tapered rifle cases, for the reasons desi suggested, having full-length resized cases too much.

But you are asking of revolver rounds.

Are you asking about the difference in diameter of the case about 3/16" ahead of the rim???

What you see there is the expansion of the case, ahead of the more solid case-head portion of the case, where the brass thins to the nominal wall thickness. It is expanded in the firing there, whereas the case-head section does not expand its diameter appreciably, and thus creates the different appearance. Not to worry, most cases do this to one degree or another, and does not affect reloading or shooting.

Or are you asking about that little dark line that goes around the case, about .020" ahead of the extractor groove?

If that, check the mouth of your chamber for burrs, or on the back of the extractor-star. That would seem to me to be the most likely culprit for that. Does it show up on every fired case, or only on cases from one chamber? Is it apparent on cases from all manufacturers or just one?

What gun are you using??? Ammo? Factory? Reloads? That's important information to those who could be of help.

And if you were using it in a rifle for Cowboy stuff, I imagine the chamber may have a slight chamfer which could make that kind of imprint.
Flash