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

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 the polytope $\Delta$. Using the stringy Libgober-Wood identity and our formula, we generalize the well-known combinatorial identity ${\sum }_{\genfrac{}{}{0ex}{}{\theta ⪯\Delta }{\dim (\theta )=1}}v(\theta )\cdot v({\theta }^{\ast })=24$ holding in the case of $3$-dimensional reflexive polytopes $\Delta$.

arXiv comment19 pages

References in corpus (5)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• Canonical toric Fano threefolds
• Weight systems for toric Calabi-Yau varieties and reflexivity of Newton polyhedra
• On the combinatorial classification of toric log del Pezzo surfaces

Cited by in corpus (1)

• Mirror symmetry for quasi-smooth Calabi-Yau hypersurfaces in weighted projective spaces