Gorenstein weak F-equivalence conjecture

Establish that every normal projective Gorenstein toric weak Fano d-fold is Gorenstein weakly F-equivalent to projective space for every integer d≥1.

Background

The paper introduces Gorenstein weak F-equivalence by enlarging Sato’s smooth relation: intermediate varieties may be singular normal projective Gorenstein toric weak Fano varieties, and consecutive varieties may be connected by projective torus-equivariant birational morphisms in either direction. This formulation is designed to overcome the smooth counterexamples that disprove Sato’s original conjecture.

The conjecture is proved in dimension three and for the centered-simplex family in all dimensions, but the general assertion is not established. Its significance is reinforced by the fact that it would imply connectedness of the inclusion graph of reflexive polytopes in each dimension.