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arXiv · 1807.00559

Stringy $E$-functions of canonical toric Fano threefolds and their applications

Victor Batyrev·Karin Schaller
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Abstract

Let $Δ$ 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 $X_Δ$ associated with the polytope $Δ$. Using the stringy Libgober-Wood identity and our formula, we generalize the well-known combinatorial identity $\sum_{θ\preceq Δ\atop \dim (θ) =1} v(θ) \cdot v(θ^*) = 24$ holding in the case of $3$-dimensional reflexive polytopes $Δ$.

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Victor Batyrev, Karin Schaller. 2018-07-02. Stringy $E$-functions of canonical toric Fano threefolds and their applications. https://doi.org/10.1070/im8835

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