Abstract
The aim of this short note is to give an explicit description of birationally equivalent models of quartic double solids with at least one node. A quartic double solid is a double covering of ℙ3 branched along a quartic surface. The nodes of the double solid are in bijection with the nodes of the quartic surface B ⊂ ℙ3. Using the projection ℙ 3 → ℙ2, whose center is a node of B, we obtain a birational map to a conic bundle over ℙ2 . We shall explicitly describe a birational equivalence between such a conic bundle and a cubic hypersurface in ℙ4. We obtain this by projecting the cubic from a smooth point.
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