My apartment/My nest

I have just realized today that there is a bird nest in my balcony. Now, as you may have concluded, I do not often get out to my balcony, although the view from the 14th floor I live is great and the weather is getting better and better.
Anyway, for the past couple of weeks I have been seeing some pigeons standing on the edge of the balcony, but I did not pay any attention. So, you can imagine my surprise today when I opened the balcony door and I found a little nest behind it (A very inconspicuous place, don't you agree?).Not only that, but inside the nest there was a little white egg!! However, the mother was not there.
Right now, the mother is sitting on the egg, and I face a problem; what to do?
As I got out to the balcony today, I realized that there was a lot of pigeon poop all over the place and I imagine things will get worse.
If there was no egg, I would probably destroy the nest but now this is not an option.
Any ideas?