Pigeons are a problem whether they enter the building or not.  Their
droppings are acidic and will etch stone, but more important for
museums, they are a terrific source of pests, especially dermestids (see
for example, Hancock, E.G. 1993.  Museum pests from pigeon nests.
Journal of Biological Curation 1(3/4):41-43).  Unfortunately, the options
for dealing with them are limited and often unsavory.  They break down
as follows:
1.  Trap the pigeons (easily done, but then you must decide to kill
them or release them elsewhere to be someone else's problem)
2.  Netting to keep them from alighting or nesting on your building.
There are some very fine plastic nets available that do not detract
too much from your building, but they are all light sensitive and must
be replaced every few months or a year.
3.  Spikes and other obstacles--these also collect wind-blown trash and
are often ineffective.
4.  Sticky stuff to put out on ledges.  This is fairly effective, but
will also trap other birds and can lead to bird deaths.
5.  Control chemicals, such as Ornitrol or Avitrol.  These must be
applied regularly, which means you are actually feeding the birds you
want to be rid of.  Expect a few overdoses, which can mean unpleasant
pigeon death agony on your front lawn.
 
We have greatly reduced a pigeon problem on our building by a combination
of trapping on occasion, obstacles (spikes plus set rat-traps, which make
a loud noise), and most important, removal of nests and eggs to cause
a population crash.
 
Good luck, but be careful or your pigeon control efforts can turn into
a public relations nightmare.
 
John Simmons
Museum of Natural History
University of Kansas