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We denote byFPMCthe class of all non-singular projective algebraic surfacesXover ℂ with finite polyhedral Mori cone NE(X) ⊂ NS(X) ⊗ ℝ. Ifρ(X) = rk NS(X) ≥ 3, then the set Exc(X) of all exceptional curves onX∈FPMCis finite and generates NE(X). LetδE(X) be the maximum of (-C2) andpE(X) the maximum ofpa(C) respectively for allC∈ Exc(X). For fixedρ≥ 3,δEandpEwe denote byFPMCρ,δE,pEthe class of all algebraic surfacesX∈FPMCsuch thatρ(X) =ρ, δE(X) =δEandpE(X) =pE. We prove that the classFPMCρ,δE,pEisdoi:10.1017/s0027763000007194 fatcat:rkqh6rk5yjbpjg4amrfbzery3q