Tangent conics at quartic surfaces and conics in quartic double solids

For a quartic double solid Z phi under right arrow P-3 we study the parameter space of conics (i.e. of smooth rational curves C subset of Z such that C.phi*O-P3(1) = 2) This parameter space is naturally fibred (with disconnected fibres) over P-3. We study the monodromy of the fibres and determine this way the irreducible components of the parameter space.