A simply connected surface of general type with $p_g=0$ and $K^2=4$

Abstract

As a continuation of the recent results of Y Lee and the second author [Invent. Math. 170 (2007) 483-505] and the authors [Geom. Topol. 13 (2009) 743-767], we construct a simply connected minimal complex surface of general type with $p_g=0$ and $K^2=4$ by using a rational blow-down surgery and $\mathbb{Q}$–Gorenstein smoothing theory.