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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.
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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
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\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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This publication is cited in the following articles:
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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, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248
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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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A. A. Borisov, L. A. Borisov, “Singular toric Fano varieties”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 277–283
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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
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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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