# A COMPLEX SURFACE OF GENERAL TYPE WITH pg=0, K2=3 AND H1 = ℤ/2ℤ

• Park, Hee-Sang ;
• Park, Jong-Il ;
• Shin, Dong-Soo
• Published : 2010.11.30
• 66 7

#### Abstract

As the sequel to our previous work [4], we construct a minimal complex surface of general type with $p_g=0$, $K^2=3$ and $H_1$ = $\mathbb{Z}/2\mathbb{Z}$ by using a rational blow-down surgery and $\mathbb{Q}$-Gorenstein smoothing the-ory.

#### Keywords

$\mathbb{Q}$-Gorenstein smoothing;rational blow-down;surface of general type

#### References

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2. Y. Lee and J. Park, A simply connected surface of general type with $p_g$ = 0 and $K^2$ = 2, Invent. Math. 170 (2007), no. 3, 483-505. https://doi.org/10.1007/s00222-007-0069-7
3. Y. Lee and J. Park, A complex surface of general type with $p_g$ = 0, $K^2$ = 2 and $H_1$ = Z/2Z, Math. Res. Lett. 16 (2009), no. 2, 323-330. https://doi.org/10.4310/MRL.2009.v16.n2.a9
4. H. Park, J. Park, and D. Shin, A simply connected surface of general type with $p_g$ = 0 and $K^2$ = 3, Geom. Topol. 13 (2009), no. 2, 743-767. https://doi.org/10.2140/gt.2009.13.743
5. U. Persson, Configurations of Kodaira fibers on rational elliptic surfaces, Math. Z. 205 (1990), no. 1, 1-47. https://doi.org/10.1007/BF02571223

#### Cited by

1. Godeaux, Campedelli, and surfaces of general type with χ=4 and 2≤K2≤8 2017, https://doi.org/10.1002/mana.201500445
2. Involutions on surfaces with p g  = q = 0 and K 2 = 3 vol.157, pp.1, 2012, https://doi.org/10.1007/s10711-011-9612-1
3. Construction of surfaces of general type from elliptic surfaces via $${\mathbb{Q}}$$ -Gorenstein smoothing vol.272, pp.3-4, 2012, https://doi.org/10.1007/s00209-012-0985-0
4. NEW EXAMPLES OF CALABI–YAU 3-FOLDS AND GENUS ZERO SURFACES vol.16, pp.02, 2014, https://doi.org/10.1142/S0219199713500107

#### Acknowledgement

Supported by : Korean Government, Research Foundation of Korea