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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 5, Pages 1032–1050 (Mi izv1216)  

This article is cited in 7 scientific papers (total in 7 papers)

Del Pezzo surfaces with log-terminal singularities. II

V. V. Nikulin


Abstract: If $Z$ is a del Pezzo surface with log-terminal singularities of index dividing $k$ and $\sigma\colon Y\to Z$ the minimal resolution of singularities of $Z$, we prove the inequality $\operatorname{rk Pic}Y<Ak^{7/2}$, where $A$ is an absolute constant. It follows from this that for fixed $k$ there are only a finite number of possible intersection graphs of all exponential curves on $Y$. In Part I these results were obtained under a certain restriction on the singularities.
The proof uses methods taken from the theory of reflection groups in Lobachevsky space.
Bibliography: 14 titles.

Full text: PDF file (2722 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:2, 355–372

Bibliographic databases:

UDC: 512.774
MSC: Primary 14J26; Secondary 14J05, 14J17, 14J25, 14E30, 51F15
Received: 04.03.1988

Citation: V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. II”, Izv. Akad. Nauk SSSR Ser. Mat., 52:5 (1988), 1032–1050; Math. USSR-Izv., 33:2 (1989), 355–372

Citation in format AMSBIB
\Bibitem{Nik88}
\by V.~V.~Nikulin
\paper Del Pezzo surfaces with log-terminal singularities.~II
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 5
\pages 1032--1050
\mathnet{http://mi.mathnet.ru/izv1216}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=972094}
\zmath{https://zbmath.org/?q=an:0677.14008}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 2
\pages 355--372
\crossref{https://doi.org/10.1070/IM1989v033n02ABEH000836}


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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. V. A. Alexeev, “Fractional indices of log Del Pezzo surfaces”, Math. USSR-Izv., 33:3 (1989), 613–629  mathnet  crossref  mathscinet  zmath
    2. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. III”, Math. USSR-Izv., 35:3 (1990), 657–675  mathnet  crossref  mathscinet  zmath
    3. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248  mathnet  crossref  mathscinet  zmath  isi
    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. A. A. Borisov, L. A. Borisov, “Singular toric Fano varieties”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 277–283  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. M. V. Degtyarev, “A bound on the Picard number of a resolution of singularities of the Fano $\operatorname{SL}(2)$-variety”, Russian Math. Surveys, 51:2 (1996), 324–325  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. Hideo Kojima, Takeshi Takahashi, “Normal del Pezzo surfaces of rank one with log canonical singularities”, Journal of Algebra, 360 (2012), 53  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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