A complex surface of general type with $p_g=0$, $K^2=4$, and $\pi_1=\mathbb{Z}/2\mathbb{Z}$

Heesang Park

A complex surface of general type with $p_g=0$, $K^2=4$, and $\pi_1=\mathbb{Z}/2\mathbb{Z}$

Algebraic Geometry 2009-11-03 v2 Geometric Topology

Authors: Heesang Park

Abstract

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 $\pi_1=\mathbb{Z}/2\mathbb{Z}$ .

Keywords

complex surface of general type rational blow-down surgery Q-Gorenstein smoothing symplectic 4-manifold fundamental group minimal surface

Cite

@article{arxiv.0910.3476,
  title  = {A complex surface of general type with $p_g=0$, $K^2=4$, and $\pi_1=\mathbb{Z}/2\mathbb{Z}$},
  author = {Heesang Park},
  journal= {arXiv preprint arXiv:0910.3476},
  year   = {2009}
}

Comments

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

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