A simply connected surface of general type with p(g)=0 and K-2=3

Abstract

Motivated by a recent result of Y Lee and the second author [9], we construct a simply connected minimal complex surface of general type with p(g) = 0 and K-2 = 3 using a rational blow-down surgery and Q-Gorenstein smoothing theory. In a similar fashion, we also construct a new simply connected symplectic 4-manifold with b(2)(+) = 1 and K-2 = 4.