Let Z be a del Pezzo surface with log-terminal singularities and σ: Y → Z a minimal resolution of singularities. Then the Picard number of Y satisfies ρ(Y) < N(e), where e is the maximal multiplicity of the singularities of Z and N a certain function of e. Bibliography: 18 titles.
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Vadim V. Nikulin (1990) studied this question.
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