The sign of scalar curvature on K\"ahler blowups

We show that if (M,ω) 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.