Proof of the oval conjecture for planar partition functions

We prove that the translation plane and the shift plane defined by a planar partition function form an oval pair of projective planes, in the sense that the planes share a line pencil and any line of either plane not in this pencil forms an oval in the other plane. This is achieved by building upon substantial work of Betten–Löwen and by using Rabier’s fibration theorem, which allows one to conclude — without the assumption of properness — that certain local diffeomorphisms are covering maps.