#### Volume 13, issue 2 (2009)

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A simply connected surface of general type with $p_g=0$ and $K^2=3$

### Heesang Park, Jongil Park and Dongsoo Shin

Geometry & Topology 13 (2009) 743–767
##### Abstract

Motivated by a recent result of Y Lee and the second author [Invent. Math. 170 (2007) 483-505], we construct a simply connected minimal complex surface of general type with ${p}_{g}=0$ and ${K}^{2}=3$ using a rational blow-down surgery and $ℚ$–Gorenstein smoothing theory. In a similar fashion, we also construct a new simply connected symplectic $4$–manifold with ${b}_{2}^{+}=1$ and ${K}^{2}=4$.

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