Geodesic
Del Pezzo surfaces with log-terminal singularities.~II
Izvestiya. Mathematics , Tome 33 (1989) no. 2, pp. 355-372

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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 $\operatorname{rk\,Pic}Y$, 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. 
@article{IM2_1989_33_2_a6,
     author = {V. V. Nikulin},
     title = {Del {Pezzo} surfaces with log-terminal {singularities.~II}},
     journal = {Izvestiya. Mathematics },
     pages = {355--372},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a6/}
}
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V. V. Nikulin. Del Pezzo surfaces with log-terminal singularities.~II. Izvestiya. Mathematics , Tome 33 (1989) no. 2, pp. 355-372. http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a6/