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Mat. Sb., 1989, Volume 180, Number 2, Pages 226–243 (Mi msb1607)  

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 $Z$.
Bibliography: 25 titles.

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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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\by V.~V.~Nikulin
\paper Del Pezzo surfaces with log-terminal singularities
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 2
\pages 226--243
\mathnet{http://mi.mathnet.ru/msb1607}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=993456}
\zmath{https://zbmath.org/?q=an:0704.14030|0674.14024}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 66
\issue 1
\pages 231--248
\crossref{https://doi.org/10.1070/SM1990v066n01ABEH001314}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990DK06800013}


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    This publication is cited in the following articles:
    1. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. II”, Math. USSR-Izv., 33:2 (1989), 355–372  mathnet  crossref  mathscinet  zmath
    2. V. A. Alexeev, “Fractional indices of log Del Pezzo surfaces”, Math. USSR-Izv., 33:3 (1989), 613–629  mathnet  crossref  mathscinet  zmath
    3. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. III”, Math. USSR-Izv., 35:3 (1990), 657–675  mathnet  crossref  mathscinet  zmath
    4. V. V. Nikulin, “Algebraic three-folds and the diagram method”, Math. USSR-Izv., 37:1 (1991), 157–189  mathnet  crossref  mathscinet  zmath  adsnasa
    5. R. Blache, “Two aspects of log terminal surface singularities”, Abh Math Semin Univ Hambg, 64:1 (1994), 59  crossref  mathscinet  zmath
    6. Nikulin V., “On the Picard Number of Fano 3-Folds with Terminal Singularities”, J. Math. Kyoto Univ., 34:3 (1994), 495–529  mathscinet  zmath  isi
    7. R. Blache, “Riemann-Roch theorem for normal surfaces and applications”, Abh Math Semin Univ Hambg, 65:1 (1995), 307  crossref  mathscinet  zmath
    8. 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  crossref  mathscinet  zmath  isi
    9. Yu. G. Prokhorov, V. V. Shokurov, “The first main theorem on complements: from global to local”, Izv. Math., 65:6 (2001), 1169–1196  mathnet  crossref  crossref  mathscinet  zmath  elib
    10. Lin, JY, “Birational unboundedness of Q-Fano threefolds”, International Mathematics Research Notices, 2003, no. 6, 301  isi
    11. 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  crossref  mathscinet  zmath  isi
    12. Okada T., “On the Birational Unboundedness of Higher Dimensional Q-Fano Varieties”, Math. Ann., 345:1 (2009), 195–212  crossref  mathscinet  zmath  isi
    13. 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  crossref  mathscinet  zmath  isi
    14. Hideo Kojima, Takeshi Takahashi, “Normal del Pezzo surfaces of rank one with log canonical singularities”, Journal of Algebra, 360 (2012), 53  crossref
    15. G. D. Noce, “On the Picard Number of Singular Fano Varieties”, International Mathematics Research Notices, 2012  crossref
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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