Abstract:
Let $\Delta$ be a $3$-dimensional lattice polytope containing exactly one
interior lattice point. We give a simple combinatorial formula for computing
the stringy $E$-function of the $3$-dimensional canonical toric Fano variety
$X_{\Delta}$ associated with $\Delta$. Using the stringy
Libgober–Wood identity and our formula, we generalize the well-known
combinatorial identity $\sum_{\substack{\theta \preceq \Delta\\ \dim
(\theta) =1}}v(\theta) \cdot v(\theta^*) = 24$ which holds for $3$-dimensional reflexive polytopes $\Delta$.