On the Singularities of Surfaces Ruled by Conics

We classify the singularities of a surface ruled by conics: they are rational double points of type A _n or D _n . This is proved by showing that they arise from a precise series of blow-ups of a suitable surface geometrically ruled by conics. We determine also the family of such surfaces which are birational models of a given surface ruled by conics and obtained in a “minimal way” from it.