Another description of certain quartic double solids

The aim of this short note is to give an explicit description of birational ly equivalent models of quartic double solids with at least one node. A qua rtic double solid is a double covering of P-3 branched along a quartic surf ace. The nodes of the double solid are in bijection with the nodes of the q uartic surface B subset of P-3. Using the projection P-3 --> P-2, whose cen ter is a node of B, we obtain a birational map to a conic bundle over P-2. We shall explicitly describe a birational equivalence between such a conic bundle and a cubic hypersurface in P-4. We obtain this by projecting the cu bic from a smooth point.