Construction of surfaces of general type from elliptic surfaces via Q-Gorenstein smoothing

Abstract

We present methods to construct interesting surfaces of general type via $\mathbb{Q}$-Gorenstein smoothing of a singular surface obtained from an elliptic surface. By applying our methods to special Enriques surfaces, we construct new examples of a minimal surface of general type with $p_g=0$, ${\pi }_1=\mathbb{Z}/2\mathbb{Z}$, and $K^2\le 4$.

This paper combines two preprints arXiv:1008.1222 and arXiv:0910.3476. The results are slightly improved

References in corpus (2)

• A simply connected surface of general type with p_g=0 and K^2=2
• The classification of minimal product-quotient surfaces with $p_g=0$