A complex surface of general type with $p_g=0$, $K^2=4$, and ${\pi }_1=\mathbb{Z}/2\mathbb{Z}$

Abstract

We construct a minimal complex surface of general type with $p_g=0$, $K^2=4$, and ${\pi }_1=\mathbb{Z}/2\mathbb{Z}$ using a rational blow-down surgery and a $\mathbb{Q}$-Gorenstein smoothing theory. In a similar fashion, we also construct a symplectic 4-manifold with $b_2^{+}=1$, $K^2=5$, and ${\pi }_1=\mathbb{Z}/2\mathbb{Z}$.

9 pages, 8 figures; Added Section 4; Corrected typos