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A complex surface of general type with $ p_g=0$, $ K^2=2$ and $ H_1=\mathbb{Z}/4\mathbb{Z}$


Authors: Heesang Park, Jongil Park and Dongsoo Shin
Journal: Trans. Amer. Math. Soc. 365 (2013), 5713-5736
MSC (2010): Primary 14J29; Secondary 14J10, 14J17, 53D05
Published electronically: January 28, 2013
MathSciNet review: 3091262
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Abstract: We construct a new minimal complex surface of general type with $ p_g=0$, $ K^2=2$ and $ H_1=\mathbb{Z}/4\mathbb{Z}$ (in fact, $ \pi _1^{\text {alg}}=\mathbb{Z}/4\mathbb{Z}$), which settles the existence question for numerical Campedelli surfaces with all possible algebraic fundamental groups. The main techniques involved in the construction are a rational blow-down surgery and a $ \mathbb{Q}$-Gorenstein smoothing theory.


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Additional Information

Heesang Park
Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Korea
Email: hspark@kias.re.kr

Jongil Park
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea – and – Korea Institute for Advanced Study, Seoul 130-722, Korea
Email: jipark@snu.ac.kr

Dongsoo Shin
Affiliation: Department of Mathematics, Chungnam National University, Daejeon 305-764, Korea
Email: dsshin@cnu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05696-6
Keywords: $\mathbb{Q}$-Gorenstein smoothing, rational blow-down surgery, surface of general type
Received by editor(s): February 21, 2011
Received by editor(s) in revised form: August 8, 2011, and August 9, 2011
Published electronically: January 28, 2013
Article copyright: © Copyright 2013 American Mathematical Society