Tangent Conics at Quartic Surfaces and Conics in Quartic Double Solids

For a quartic double solid we study the parameter space of conics (i.e. of smooth rational curves C ⊂ Z such that C · φ*O(1) = 2). This parameter space is naturally fibred (with disconnected fibres) over Pˇ³. We study the monodromy of the fibres and determine this way the irreducible components of the parameter space.