Estimated transversality and rational maps
Abstract
Description
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.
40 pages, submitted, typos corrected and minor expository changes
40 pages, submitted, typos corrected and minor expository changes