How to assemble .NET Core project under ubuntu in a single file?

There's something about this, but I would say it's not quite something and while it's in pre-alpha state. The end result is one of "bold" Executive file.

UPD. Still have this, but the campaign there will be even more crutches

In theory, you can build deb-package, which will be your app.
Still, it is possible to look here - https://docs.snapcraft.io/build-snaps/your-first-snap

This applies not only to Core Ubuntu. To normal .Net under Windows, too.
Solve this problem by adding all the dependencies of the executable file (for example .exe) in resources of this .exe. Then when you run the application registers an event handler for the AppDomain.AssemblyResolve, which gets the right Assembly of resources, loads it into the domain and returns a reference to her environment. AppDomain.AssemblyResolve is called every time an application needs some kind of dependence.
It's simple and easy implemented, while it does not take much time.
There are also libraries, which are built into the build process and allow this thing to automate. The above has already been mentioned ILMerge, there's also Fody, there are some analogues.