Core dumps are used by the developers for debugging an executable.
They are created when programs crash.
First, delete all these files.
Then, to avoid creation of these files, you need to restrict the core dump size before the desktop initialises.
ulimit -c 0 will let you disable creation of cores, but this will only apply to processes launched from this particular instance of the bash shell.
You need to restrict core dump size before the desktop initialises, so you have to put this line in the beginning of ~/.xsession or /etc/X11/Xsession file.