Del Pezzo Surfaces With Log-Terminal Singularities. I

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 ?(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. Bibliography: 25 titles.