Theta divisors and permutohedra
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866915208455258112 |
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| author | Buchstaber, V. M. Veselov, A. P. |
| author_facet | Buchstaber, V. M. Veselov, A. P. |
| contents | We establish an intriguing relation of the smooth theta divisor $Θ^n$ with permutohedron $Π^n$ and the corresponding toric variety $X_Π^n.$ In particular, we show that the generalised Todd genus of the theta divisor $Θ^n$ coincides with $h$-polynomial of permutohedron $Π^n$ and thus is different from the same genus of $X_Π^n$ only by the sign $(-1)^n.$ As an application we find all the Hodge numbers of the theta divisors in terms of the Eulerian numbers. We reveal also interesting numerical relations between theta-divisors and Tomei manifolds from the theory of the integrable Toda lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16042 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Theta divisors and permutohedra Buchstaber, V. M. Veselov, A. P. Algebraic Topology Algebraic Geometry 14F45, 14M25, 55NXX We establish an intriguing relation of the smooth theta divisor $Θ^n$ with permutohedron $Π^n$ and the corresponding toric variety $X_Π^n.$ In particular, we show that the generalised Todd genus of the theta divisor $Θ^n$ coincides with $h$-polynomial of permutohedron $Π^n$ and thus is different from the same genus of $X_Π^n$ only by the sign $(-1)^n.$ As an application we find all the Hodge numbers of the theta divisors in terms of the Eulerian numbers. We reveal also interesting numerical relations between theta-divisors and Tomei manifolds from the theory of the integrable Toda lattice. |
| title | Theta divisors and permutohedra |
| topic | Algebraic Topology Algebraic Geometry 14F45, 14M25, 55NXX |
| url | https://arxiv.org/abs/2211.16042 |