Kodaira Dimension of Fiber Sums along Spheres.

link: http://arxiv.org/abs/1008.4447
Abstract

In this note we discuss the effect of the symplectic sum along spheres in
symplectic four-manifolds on the Kodaira dimension of the underlying symplectic
manifold. We find that the Kodaira dimension is non-decreasing. Moreover, we
are able to obtain precise results on the structure of the manifold obtained
from the blow down of an embedded symplectic -4-sphere.