- Putting software under the GPL does not mean abandoning ownership?
Absolutely not. In nations signatory to the Berne Convention, copyright is the default, which means by default only the author (or current copyright holder, if the original author transfers the copyright) may reproduce the work, prepare derivative works, etc.
The author of a work may use a license to permit other people to use the work in specific ways, subject to author-defined license-specific rules. Allowing other people to use the work via a license in no way lessens the author's copyright -- on the contrary, the author's copyright is what makes the license possible and necessary.
It is important to note that any recipient of a GPL-licensed work can distribute and modify it. Thus, even if the author stops distributing a GPL-licensed work, the author cannot rescind the rights previously granted to existing recipients. (This claim is somewhat debated for GPLv2, and may vary by jurisdiction, but is made explicit in GPLv3.) Inthat sense, releasing a work under the GPL means abandoning the ability to restrict its distribution, but this is tremendously different from abandoning ownership.
- What constitutes ownership? Is it the copyright?
Yes, copyright is a kind of "ownership," in the metaphorical mapping of intellectual property rights onto physical property rights. That is, the copyright holder of a work has certain exclusive rights to a work. Those rights can be granted in limited ways (or unlimited ways, if you're feeling generous) to other people, but ultimately the grant of those rights comes from the legal reality that those rights fundamentally belong to the copyright holder, to be licensed as the copyright holder pleases.
- The owner is not bound by the GPL, e.g. he could change or improve the code without having to share the changes back to the community?
Absolutely. The copyright holder is not beholden to the rules of the holder's own license grant. The copyright holder's rights stem from copyright law, not from a license grant. The copyright holder can legally prepare a derivative work based on copyright rights. Other people can prepare derivative works of someone else's work only insofar as the right to do so is licensed to them. In the case of the GPL, that means that others' derivative works must be GPL-licensed. the copyright holder need not follow this rule.
- What about community contributions? Whom do they belong to? If not clearly defined, what options do exist?
Technically speaking, a contribution in isolation (e.g., in a diff format, showing what characters to add or remove) is not a derivative work and its creator holds the copyright to the contribution. However, a complete modified project that incorporates that change is a derivative work. In order to distribute that modified work (assuming a GPL-licensed base project), the distributor must follow the rules of the GPL; i.e., the changes must be licensed under the GPL as well.