  We show that an earlier conjecture of the author, on diophantine
approximation of rational points on varieties, implies the ``abc conjecture''
of Masser and Oesterl'e. In fact, a weak form of the former conjecture is
sufficient, involving an extra hypothesis that the variety and divisor admit a
faithful group action of a certain type. Analogues of this weaker conjecture
are proved in the split function field case of characteristic zero, and in the
case of holomorphic curves (Nevanlinna theory).
  The proof of the latter involves a geometric generalization of the classical
lemma on the logarithmic derivative, due to McQuillan. This lemma may be of
independent interest.
