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Mat. Zametki, 2008, Volume 83, Issue 2, Pages 170–180 (Mi mz3833)  

This article is cited in 9 scientific papers (total in 9 papers)

Del Pezzo Surfaces with Log Terminal Singularities

G. N. Belousov

M. V. Lomonosov Moscow State University

Abstract: We prove that there are no del Pezzo surfaces with five log terminal singularities and the Picard number 1. In the course of the proof, we make use of fibrations with general fiber $\mathbb P^1$.

Keywords: algebraic surface, del Pezzo surface, log terminal singularity, anticanonical class, Picard number, canonical divisor, ruled surface

DOI: https://doi.org/10.4213/mzm3833

Full text: PDF file (472 kB)
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English version:
Mathematical Notes, 2008, 83:2, 152–161

Bibliographic databases:

UDC: 512.6
Received: 10.10.2006

Citation: G. N. Belousov, “Del Pezzo Surfaces with Log Terminal Singularities”, Mat. Zametki, 83:2 (2008), 170–180; Math. Notes, 83:2 (2008), 152–161

Citation in format AMSBIB
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\paper Del Pezzo Surfaces with Log Terminal Singularities
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\yr 2008
\vol 83
\issue 2
\pages 170--180
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\pages 152--161
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  • http://mi.mathnet.ru/eng/mz/v83/i2/p170

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Belousov G., “The maximal number of singular points on log del Pezzo surfaces”, J. Math. Sci. Univ. Tokyo, 16:2 (2009), 231–238  mathscinet  zmath  isi
    2. Hwang D., Keum J., “The maximum number of singular points on rational homology projective planes”, J. Algebraic Geom., 20:3 (2011), 495–523  crossref  mathscinet  zmath  isi
    3. Kojima H., Takahashi T., “Normal del Pezzo surfaces of rank one with log canonical singularities”, J. Algebra, 360 (2012), 53–70  crossref  mathscinet  zmath  isi  elib  scopus
    4. Kojima H., “Supplement to “Normal del Pezzo surfaces of rank one with log canonical singularities” by H. Kojima and T. Takahashi [J. Algebra 360 (2012) 53–70]”, J. Algebra, 377 (2013), 312–316  crossref  mathscinet  zmath  isi
    5. Hwang D., Keum J., “Algebraic Montgomery-Yang Problem: the Log Del Pezzo Surface Case”, J. Math. Soc. Jpn., 66:4 (2014), 1073–1089  crossref  mathscinet  zmath  isi  scopus
    6. Hwang D., “On the Orbifold Euler Characteristic of Log Del Pezzo Surfaces of Rank One”, J. Korean. Math. Soc., 51:4 (2014), 867–879  crossref  mathscinet  zmath  isi  scopus
    7. DongSeon H., JongHae K., Hisanori O., “Gorenstein Q-Homology Projective Planes”, Sci. China-Math., 58:3, SI (2015), 501–512  crossref  mathscinet  zmath  isi  scopus
    8. Lai Ch.-J., “Bounding Volumes of Singular Fano Threefolds”, Nagoya Math. J., 224:1 (2016), 37–73  crossref  mathscinet  zmath  isi  scopus
    9. Lin Ch.-Y., “A Non-vanishing Theorem of Del Pezzo Surfaces”, Proc. Edinb. Math. Soc., 59:2 (2016), 463–472  crossref  mathscinet  zmath  isi  elib  scopus
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