  In this paper, we address a question of Donaldson's on the best estimate that
can be achieved for the transversality of an asymptotically holomorphic
sequence of sections of increasing powers of a line bundle over an integral
symplectic manifold. More specifically, we find an upper bound for the
transversality of n such sequences of sections over a 2n-dimensional symplectic
manifold. In the simplest case of S^2, we also relate the problem to a well
known question in potential theory (namely, that of finding logarithmic
equilibrium points), thus establishing an experimental lower bound for the
transversality.
