Estimated transversality and rational maps

Details Estimated transversality and rational maps Estimated transversality and rational maps

2005-11-29

arxiv.org/abs/math/0511716v2

Mathematics

Symplectic Geometry

40 pages, submitted, typos corrected and minor expository changes

Scientific paper

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.

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