Geodesic
Del Pezzo surfaces with nonrational singularities
Matematičeskie zametki, Tome 62 (1997) no. 3, pp. 451-467

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Normal algebraic surfaces $X$ with the property $\operatorname{rk}(\operatorname{Div}(X)\otimes\mathbb Q/{\equiv})=1$, numerically ample canonical classes, and nonrational singularities are classified. It is proved, in particular, that any such surface $X$ is a contraction of an exceptional section of a (possibly singular) relatively minimal ruled surface $\widetilde X$ with a nonrational base. Moreover, $\widetilde X$ is uniquely determined by the surface $X$. 
@article{MZM_1997_62_3_a13,
     author = {I. A. Cheltsov},
     title = {Del {Pezzo} surfaces with nonrational singularities},
     journal = {Matemati\v{c}eskie zametki},
     pages = {451--467},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_3_a13/}
}
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I. A. Cheltsov. Del Pezzo surfaces with nonrational singularities. Matematičeskie zametki, Tome 62 (1997) no. 3, pp. 451-467. http://geodesic.mathdoc.fr/item/MZM_1997_62_3_a13/