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

MathSciNet review:
2888175

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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.

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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

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.