Del Pezzo surfaces with log-terminal singularities

A new method is applied to the study of del Pezzo surfaces $Z$ with log-terminal singularities, taken from the theory of reflection groups in Lobachevsky space. This method yields bounds on the Picard number $\rho(Y)$ of a minimal resolution $Y$ of singularities of $Z$, assuming that the indices or the multiplicities of the singularities of $Z$ are bounded, and under an extra (conjecturally inessential) condition of generality on the singularities of $Z$.
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