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# Journal of Symplectic Geometry

## Volume 4 (2006)

### Number 2

### Estimated transversality and rational maps

Pages: 199 – 236

DOI: http://dx.doi.org/10.4310/JSG.2006.v4.n2.a4

#### Author

#### Abstract

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 $n + 1$ such sequences of sections over a $2n$-dimensional symplectic manifold. In the simplest case of $S\sp 2$, 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.

#### 2010 Mathematics Subject Classification

53Dxx