Ample Weil divisors on K3 surfaces with Du Val singularities (Q1190833)

Following previous results [\textit{B. Saint-Donat}, Am. J. Math. 96, 602- 639 (1974; Zbl 0301.14011)] concerning nonsingular Fano varieties and \(K3\) surfaces the author considers singular \(\mathbb{Q}\)-Fano varieties. Mainly he proves: If \(D\) is an ample Weil divisor on a \(K3\) surface with Du Val singularities and the Picard number for a general element \(S\) in the ample anticanonical class \(-K_ X\), is \(\rho(S)=1\) and one of the following two inequalities is true \(D^ 2>12{25\over 42}\) or \(h^ 0(D)>7\), then the linear system \(| D|\) does not have multiple base curves, i.e. multiple base components of \(| D|\).