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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Construction of singular rational surfaces of Picard number one with ample canonical divisor
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by DongSeon Hwang and JongHae Keum
Proc. Amer. Math. Soc. 140 (2012), 1865-1879
DOI: https://doi.org/10.1090/S0002-9939-2011-11038-4
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.
References
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Bibliographic 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
  • MR Author ID: 291447
  • Email: jhkeum@kias.re.kr
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1865-1879
  • MSC (2010): Primary 14J17, 14J26
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11038-4
  • MathSciNet review: 2888175