Duality for tensor-generating fans

Determine whether there exists an involution on the class of tensor-generating complete fans that extends polar duality for reflexive polytopes.

Background

Polar duality is an involution on the set of reflexive polytopes. The paper introduces tensor-generating fans as a broader combinatorial class associated with tensor-generating canonical bundles, and notes that tensor-generation is a property of the fan rather than necessarily of a single polytope. The authors leave unresolved whether this larger class possesses a comparable duality operation extending the reflexive-polytope construction.

References

We do not know whether a comparable structure organizes $\otimes$-generating fans. Is there an involution of the class of $\otimes$-generating fans extending polar duality of reflexive polytopes?

— Tensor-generating line bundles on toric varieties  (2610.22279 - Ito et al., 15 Oct 2026) in Question 2.?, immediately after Example 2.? and before Section 3 (subsection on the curve criterion)