Slawomir Cynk

Title: Orphan double octic Calabi-Yau manifolds
(joint work with D. van Straten)

Abstract:
Computation of Picard-Fuchs operators for 61 one-parameter families of 
double octic Calabi-Yau threefolds exhibited 25 cases without a point of 
Maximal Unipotent Monodromy (MUM). First examples of this kind where 
constructed by J.C. Rohde and later by A. Garbagnati and B. van Geemen. 
However in all these examples the local system decomposes
and consequently the Picard-Fuchs operator has order 2.

Among the 25 orphan (as W. Zudilin suggested to call operators without a 
MUM) families there are seven cases with Picard-Fuchs operator of order 
2. I will present classification of 18 order four Picard-Fuchs operators 
without a MUM based on a reduction to the simplest form.