Birational models of terminal sextic double solids

We study sextic double solids, which are double covers of ℙ^3 branched along a sextic surface. We impose that such a 3-fold carries an isolated compound A_n singularity, abbreviated by cA_n. We first prove the bound n ≤ 8 for having an isolated cA_n singularity. We then explicitly parametrize sextic double solids with an isolated cA_n singularity and show that general sextic double solids with a cA_n point with n ≥ 4 are birationally non-rigid viewed as Mori fibre spaces. Birational non-rigidity is shown by constructing Sarkisov links starting with an extremal divisorial extraction from the singular point in each case.