The authenticity database said if you shine an ultraviolet light on authentic ancient pottery, it reflects the light evenly; if it's been repaired, the different parts of the pottery shine differently.
Hint 2
There are black lights all over the place in the Underworld, but the only one you could look at closely was under Cerberus's foot.
Hint 3
When you look at it now, Nancy says she needs a wrench --
Hint 4
-- which you can now find in the Workshop, on the table on the right (where you got charcoal earlier).
Hint 5
Use the hex wrench on the blacklight, then use the blacklight on the pot in question; it's in the pottery display in the museum.
Hint 6
I'm not sure what Nancy sees that makes her so sure the vase is a fake, but let's take her word for it. After you use the blacklight, talk to Grigor, then Xenia, then Niobe in the Workshop --
Hint 7
-- whom you overhear having a tense discussion with Thanos. She then says she left you something on the stage, so go get it.
Hint 8
If you can't find it, stand on the lift door and look closely at the stone cylinders to the left; pick up one of the daffodils to get a key --