Surfaces of general type with $p_g=1$ and $q=0$

Abstract

In this paper we construct a new family of simply connected minimal complex surfaces of general type with $p_g=1$, $q=0$, and $K^2=3,4,5,6,8$ using a $\mathbb{Q}$-Gorenstein smoothing theory. We also reconstruct minimal complex surfaces of general type with $p_g=1$, $q=0$, and $K^2=1,2$ using the same method.

21 pages, 29 figures. Title changed. This paper combines two preprints arXiv:0906.5195 and arXiv:0910.3506

References in corpus (2)

• On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$
• A construction of Horikawa surface via Q-Gorenstein smoothings

Cited by in corpus (4)

• Construction of surfaces of general type from elliptic surfaces via Q-Gorenstein smoothing
• Extending symmetric determinantal quartic surfaces
• A simply connected surface of general type with $p_g=1$, $q=0$, and $K^2=8$
• On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$