To own the copyright in it? Blockchain doesn't really do much here because ownership of copyrights is determined by the legal system not by a blockchain. (And normally when an artist sells an artwork they keep the copyright themselves; you only get the copyright too if you specifically negotiate with the artist for that, or if you commission the art as a "work-for-hire".)

To own the only digital copy of it? Blockchain does nothing to stop people making more digital copies of it. Blockchain is not a DRM system.

It seems like "owning" digital art where one doesn't have the copyright or exclusive possession of digital copies is basically a meaningless form of ownership. It is the status of "ownership" stripped of all substantive content.