What the receding ice has revealed, however, are substantial deposits of valuable gemstones waiting to be mined.
There's gold, uranium and other rare earth minerals on the island; that has been known for years, and a gold mine was established some years ago. But as that mining company found out, the cost of extraction exceeds by a rather large margin the market value. And the receding ice is a summer phenomenon; any mining operation will still be operating in winter conditions for 8 months a year, causing huge logistical issues to the point extraction is loss making. When they have to close an actual gold mine, that tells you all you need to know.
...Denmark for it, who is struggling to support it.
Struggling to support it? Surely, Sir, you're using the wrong orifice for communication!
The annual 'block' support to Greenland is in the region of 4,6BN DKK, or roughly 0,15% of the Danish GDP. Peanuts, in other words. The economy in Greenland is actually going pretty good; unemployment is below 5% and there's a burgeoning shortage of labour. If anything, the economy is in danger of overheating.
Greenland is not for sale and will not be coming up for sale. It has a fairly large level of autonomy, but will remain part of the Danish realm for the foreseeable future.
Signature. You just read one.