In philosophy, 'objective' means something like 'mind independent' while 'subjective' mean 'mind dependent'. So, yes, of course, objectivity exists.
A subjective fact: I love coffee.
An objective fact: There are chairs.
If all of the minds in the universe suddenly ceased to exist, the chairs would still be here, so it doesn't make much sense to say objective facts are just sums of all of the subjective ones. Unless you are some sort of idealist, I guess. (But nobody's an idealist anymore).
"If all of the minds in the universe suddenly ceased to exist, the chairs would still be here." I'm not so sure about that (and there is also no way to prove it) as chairs are chairs only for minds naming and using it it like that.
"objective facts are just sums of all of the subjective ones" I did not say that (did I?).
:)