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This article is cited in 15 scientific papers (total in 15 papers)
Del Pezzo surfaces with log-terminal singularities
V. V. Nikulin
Abstract:
A new method is applied to the study of del Pezzo surfaces $Z$ with log-terminal singularities, taken from the theory of reflection groups in Lobachevsky space. This method yields bounds on the Picard number $\rho(Y)$ of a minimal resolution $Y$ of singularities of $Z$, assuming that the indices or the multiplicities of the singularities of $Z$ are bounded, and under an extra (conjecturally inessential) condition of generality on the singularities of $Z$.
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English version:
Mathematics of the USSR-Sbornik, 1990, 66:1, 231–248
Bibliographic databases:
  
UDC:
512.744
MSC: Primary 14J26; Secondary 14J05, 14J17, 14J25, 14E30, 51F15, 05C99
Received: 12.01.1988
Citation:
V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Mat. Sb., 180:2 (1989), 226–243; Math. USSR-Sb., 66:1 (1990), 231–248
Citation in format AMSBIB
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\yr 1989
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\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 66
\issue 1
\pages 231--248
\crossref{https://doi.org/10.1070/SM1990v066n01ABEH001314}
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http://mi.mathnet.ru/eng/msb1607 http://mi.mathnet.ru/eng/msb/v180/i2/p226
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This publication is cited in the following articles:
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V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. II”, Math. USSR-Izv., 33:2 (1989), 355–372
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V. A. Alexeev, “Fractional indices of log Del Pezzo surfaces”, Math. USSR-Izv., 33:3 (1989), 613–629
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V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. III”, Math. USSR-Izv., 35:3 (1990), 657–675
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V. V. Nikulin, “Algebraic three-folds and the diagram method”, Math. USSR-Izv., 37:1 (1991), 157–189
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R. Blache, “Two aspects of log terminal surface singularities”, Abh Math Semin Univ Hambg, 64:1 (1994), 59
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Nikulin V., “On the Picard Number of Fano 3-Folds with Terminal Singularities”, J. Math. Kyoto Univ., 34:3 (1994), 495–529
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R. Blache, “Riemann-Roch theorem for normal surfaces and applications”, Abh Math Semin Univ Hambg, 65:1 (1995), 307
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Nikulin V., “Basis of the Diagram Method for Generalized Reflection Groups in Lobachevsky Spaces and Algebraic Surfaces with Nef Anticanonical Class”, Int. J. Math., 7:1 (1996), 71–108
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Yu. G. Prokhorov, V. V. Shokurov, “The first main theorem on complements: from global to local”, Izv. Math., 65:6 (2001), 1169–1196
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Lin, JY, “Birational unboundedness of Q-Fano threefolds”, International Mathematics Research Notices, 2003, no. 6, 301
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Dais D.I., “Classification of Toric Log Del Pezzo Surfaces Having Picard Number 1 and Index <= 3”, Results Math., 54:3-4 (2009), 219–252
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Okada T., “On the Birational Unboundedness of Higher Dimensional Q-Fano Varieties”, Math. Ann., 345:1 (2009), 195–212
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Kasprzyk A.M., Kreuzer M., Nill B., “On the Combinatorial Classification of Toric Log Del Pezzo Surfaces”, LMS J. Comput. Math., 13 (2010), 33–46
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Hideo Kojima, Takeshi Takahashi, “Normal del Pezzo surfaces of rank one with log canonical singularities”, Journal of Algebra, 360 (2012), 53
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G. D. Noce, “On the Picard Number of Singular Fano Varieties”, International Mathematics Research Notices, 2012
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