Stringy $E$-functions of canonical toric Fano threefolds and their applications
- Autores: Batyrev V.V.1, Schaller K.2
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Afiliações:
- Mathematisches Institut, Universität Tübingen
- Freie Universität Berlin
- Edição: Volume 83, Nº 4 (2019)
- Páginas: 26-49
- Seção: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133777
- DOI: https://doi.org/10.4213/im8835
- ID: 133777
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Resumo
Let $\Delta$ be a $3$-dimensional lattice polytope containing exactly oneinterior lattice point. We give a simple combinatorial formula for computingthe stringy $E$-function of the $3$-dimensional canonical toric Fano variety$X_{\Delta}$ associated with $\Delta$. Using the stringyLibgober–Wood identity and our formula, we generalize the well-knowncombinatorial identity $\sum_{\substack{\theta \preceq \Delta\dim(\theta) =1}}v(\theta) \cdot v(\theta^*) = 24$ which holds for $3$-dimensional reflexive polytopes $\Delta$.
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Sobre autores
Victor Batyrev
Mathematisches Institut, Universität Tübingen
Email: victor.batyrev@uni-tuebingen.de
Doctor of physico-mathematical sciences, Professor
Karin Schaller
Freie Universität Berlin
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