  In this article we completely determine the possible dimensions of integral
points and holomorphic curves on the complement of a union of hyperplanes in
projective space. Our main theorems generalize a result of Evertse and Gyory,
who determined when all sets of integral points (over all number fields) on the
complement of a union of hyperplanes are finite, and a result of Ru, who
determined when all holomorphic maps to the complement of a union of
hyperplanes are constant. The main tools used are the S-unit lemma and its
analytic analogue, Borel's lemma.
