A complex surface of general type with $p_g=0$, $K^2=2$ and $H_1=\mathbb {Z}/4\mathbb {Z}$
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- by Heesang Park, Jongil Park and Dongsoo Shin PDF
- Trans. Amer. Math. Soc. 365 (2013), 5713-5736 Request permission
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.References
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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
- 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
- © Copyright 2013 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 365 (2013), 5713-5736
- MSC (2010): Primary 14J29; Secondary 14J10, 14J17, 53D05
- DOI: https://doi.org/10.1090/S0002-9947-2013-05696-6
- MathSciNet review: 3091262