Hi Lothar
As someone who once owned this item, I can tell you what I think it is. I bought it believing it to be a restored paperweight, but I think that is incorrect. I believe that it was once a rare (and potentially valuable) dish on a pedestal, which was broken sometime in the past. There are a couple illustrated in the big Clichy book. The base has the remains of the facets from the top of the stem, and the deep recess is where - I suspect - a deep crack occurred, and it was repolished to make a paperweight. It is an interesting item, but very shallow: only 25mm.
Alan