A complex surface of general type with $p_g=0$, $K^2=4$, and $π_1=\mathbb{Z}/2\mathbb{Z}$

Details A complex surface of general type with $p_g=0$, $K^2=4$, and $π_1=\mathbb{Z}/2\mathbb{Z}$ A complex surface of general type with $p_g=0$, $K^2=4$, and $π_1=\mathbb{Z}/2\mathbb{Z}$

2009-10-19

arxiv.org/abs/0910.3476v2

Mathematics

Algebraic Geometry

9 pages, 8 figures; Added Section 4; Corrected typos

Scientific paper

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 and
a $\mathbb{Q}$-Gorenstein smoothing theory. In a similar fashion, we also
construct a symplectic 4-manifold with $b_2^+=1$, $K^2=5$, and
$\pi_1=\mathbb{Z}/2\mathbb{Z}$.

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