#### Volume 13, issue 3 (2009)

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

### Heesang Park, Jongil Park and Dongsoo Shin

Geometry & Topology 13 (2009) 1483–1494
##### 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 $ℚ$–Gorenstein smoothing theory.

##### Keywords
rational blow-down, $\mathbb{Q}$–Gorenstein smoothing, surface of general type
##### Mathematical Subject Classification 2000
Primary: 14J29
Secondary: 14J10, 14J17, 53D05