Gamma-positivity for smooth Gorenstein lattice polytopes

Establish that every smooth Gorenstein lattice polytope has a gamma-positive h*-polynomial.

Background

The conjecture is motivated by the combination of conjectural quadratic properties of toric ideals of smooth lattice polytopes and the Ferroni–Higashitani conjecture relating quadratic triangulations to gamma-positivity.

The paper proves this conjecture for polar duals of pseudo-symmetric smooth Fano polytopes, a particular subclass of smooth Gorenstein lattice polytopes. The general conjecture remains unresolved in the scope of the paper.

References

Every smooth Gorenstein lattice polytope has a $\gamma$-positive $h*$-polynomial.

— Magic positivity for polar duals of pseudo-symmetric smooth Fano polytopes  (2610.06419 - Ohsugi et al., 5 Oct 2026) in Conjecture 1, Section 1, Introduction