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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Construction of singular rational surfaces of Picard number one with ample canonical divisor


Authors: DongSeon Hwang and JongHae Keum
Journal: Proc. Amer. Math. Soc. 140 (2012), 1865-1879
MSC (2010): Primary 14J17, 14J26
Published electronically: October 7, 2011
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Abstract: Kollár gave a series of examples of rational surfaces of Picard number $ 1$ with ample canonical divisor having cyclic singularities. In this paper, we construct several series of new examples in a geometric way, i.e., by blowing up several times inside a configuration of curves on the projective plane and then by contracting chains of rational curves. One series of our examples has the same singularities as Kollár's examples.


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Additional Information

DongSeon Hwang
Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea
Address at time of publication: (Dongseon Hwang) Department of Mathematics, Ajou University, Suwon 443-749, Republic of Korea
Email: dshwang@kias.re.kr

JongHae Keum
Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea
Email: jhkeum@kias.re.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11038-4
PII: S 0002-9939(2011)11038-4
Keywords: Rational surface, ample canonical divisor, cyclic singularity, $\mathbb{Q}$-homology projective plane
Received by editor(s): August 9, 2010
Received by editor(s) in revised form: February 1, 2011
Published electronically: October 7, 2011
Additional Notes: This research was supported by the National Research Foundation (NRF) of Korea, funded by the Ministry of EST (2007-2-C00002).
Dedicated: In memory of the late Professor Hyo Chul Myung, the founder of KIAS
Communicated by: Lev Borisov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.