  We show that if $(M,\omega)$ is a compact K\"ahler manifold with
positive/negative scalar curvature, then the blowup of $M$ at any point also
furnishes a positive/negative scalar curvature K\"ahler metric in classes which
make the exceptional divisor small. In the case of K\"ahler surfaces with
positive scalar curvature, this extends a result of N. Hitchin to surfaces and
answers a conjecture of C. LeBrun in the affirmative, as a result completing
the classification of such surfaces.
