Higher-order Calabi–Yau operators from platonic operators

Construct new higher-order Calabi–Yau differential operators from the platonic Picard–Fuchs operators, as suggested by their possible use in Hadamard-product constructions.

Background

The paper explains that Picard–Fuchs operators associated with K3 surfaces and Calabi–Yau threefolds can have orders three and four, respectively, and that Hadamard products provide a method for constructing examples. Bradley Klee posed the question of whether the second-order platonic operators could similarly generate interesting higher-order operators. The authors state that they have not succeeded in carrying out this construction, leaving the problem unresolved.