Orphan double octics

I will discuss one parameter families of double octic Calabi-Yau threefolds wittout a point of Maximal Unipotent Monodromy, these examples are very special from the point of view of Mirror Symmetry. Among them there are seven cases with Picard-Fuchs operators of order 2 and 18 with an operator of order four. The classification of the operator is based on a careful study of singular points. Joint work with Duco van Straten (Mainz).