Geodesic
Del~Pezzo surfaces with log-terminal singularities.~III
Izvestiya. Mathematics , Tome 35 (1990) no. 3, pp. 657-675

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Let $Z$ be a del Pezzo surface with log-terminal singularities and $\sigma\colon Y\to Z$ a minimal resolution of singularities. Then the Picard number of $Y$ satisfies $\rho(Y)$, where $e$ is the maximal multiplicity of the singularities of $Z$ and $N$ a certain function of $e$. Bibliography: 18 titles. 
@article{IM2_1990_35_3_a6,
     author = {V. V. Nikulin},
     title = {Del~Pezzo surfaces with log-terminal {singularities.~III}},
     journal = {Izvestiya. Mathematics },
     pages = {657--675},
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     volume = {35},
     number = {3},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_35_3_a6/}
}
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V. V. Nikulin. Del~Pezzo surfaces with log-terminal singularities.~III. Izvestiya. Mathematics , Tome 35 (1990) no. 3, pp. 657-675. http://geodesic.mathdoc.fr/item/IM2_1990_35_3_a6/