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arXiv · 2211.16042

Theta divisors and permutohedra

V. M. Buchstaber·A. P. Veselov
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Abstract

We establish an intriguing relation of the smooth theta divisor $\Theta^n$ with permutohedron $\Pi^n$ and the corresponding toric variety $X_\Pi^n.$ In particular, we show that the generalised Todd genus of the theta divisor $\Theta^n$ coincides with $h$-polynomial of permutohedron $\Pi^n$ and thus is different from the same genus of $X_\Pi^n$ 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.

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V. M. Buchstaber, A. P. Veselov. 2022-11-29. Theta divisors and permutohedra. https://arxiv.org/abs/2211.16042

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