Calabi–Yau operators of degree two

Abstract

We show that the solutions to the equations, defining the so-called Calabi–Yau condition for fourth-order operators of degree two, define a variety that consists of ten irreducible components. These can be described completely in parametric form, but only two of the components seem to admit arithmetically interesting operators. We include a description of the 69 essentially distinct fourth-order Calabi–Yau operators of degree two that are presently known to us.