# A complex surface of general type with $p g=0$, $K^2=4$, and $π 1=mathbb{Z}-2mathbb{Z}$ - Mathematics > Algebraic Geometry

A complex surface of general type with $p g=0$, $K^2=4$, and $π 1=mathbb{Z}-2mathbb{Z}$ - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

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 anda $\mathbb{Q}$-Gorenstein smoothing theory. In a similar fashion, we alsoconstruct a symplectic 4-manifold with $b 2^+=1$, $K^2=5$, and$\pi 1=\mathbb{Z}-2\mathbb{Z}$.

Author: Heesang Park

Source: https://arxiv.org/