Links can be moved by dragging them with the mouse from one location in the file
system folder heirarchy onto the desktop.  Files and normal folders are moved
from the keyboard using Cut & Paste.  That fails with links when going onto the
desktop (though it succeeds when going into another folder):

1. Bring up Nautilus to a window/directory you have write access to.
2. Use arrow key navigation to select a file/folder
3. Press Ctrl-M to make a link to that file/folder, which is now selected
4. Press Ctrl-X to cut that link.  Note the text in the status bar: 
   link to "<filename>" will be moved if you select the Paste Files command
5. Press Ctrl-Alt-Tab to bring focus to the desktop
6. Press Ctrl-P to paste the link.  Note that it doesn't appear on the desktop.

Compare to selecting that same link in the folder heirarchy, and using the mouse
to drag it to the desktop, which works.