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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
Posted:
October 7, 2011
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References |
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Abstract: Kollár gave a series of examples of rational surfaces of Picard number  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.
References
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D. Hwang and J. Keum, Algebraic Montgomery-Yang Problem: the non-rational surface case, arXiv:0906.0633.
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D. Hwang and J. Keum, Algebraic Montgomery-Yang Problem: the log del Pezzo surface case, preprint.
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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
Posted:
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 after
28 years from publication.
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