Let A be a singular K-3
surface with hypersurface singularities. If A has singularities other than rational
singularities, then the minimal resolution of A is a ruled surface over a non-singular
algebraic curve of genus q(0 ≤ q ≤ 3), and further, under the additional
conditions q≠0 and dimH2(A;R) = 1, the global structure of M can be
determined.