Abstract
Normal algebraic surfacesX with the property rk(Div(X)⊗ℚ/≡)=1, numerically ample canonical classes, and nonrational singularities are classified. It is proved, in particular, that any such surfaceX is a contraction of an exceptional section of a (possibly singular) relatively minimal ruled surface\(\tilde X\) with a nonrational base. Moreover,\(\tilde X\)f is uniquely determined by the surfaceX.
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Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 451–467, September, 1997.
Translated by O. V. Sipacheva
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Chel’tsov, I.A. Del Pezzo surfaces with nonrational singularities. Math Notes 62, 377–389 (1997). https://doi.org/10.1007/BF02360880
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DOI: https://doi.org/10.1007/BF02360880