## Roots of Ehrhart polynomials of smooth Fano polytopes

Hegedüs, Gábor and Kasprzyk, Alexander M. (2011) Roots of Ehrhart polynomials of smooth Fano polytopes. Discrete & Computational Geometry, 46 (3). pp. 488-499. ISSN 1432-0444

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## Abstract

V. Golyshev conjectured that for any smooth polytope P of dimension at most five, the roots $z\in\C$ of the Ehrhart polynomial for P have real part equal to -1/2. An elementary proof is given, and in each dimension the roots are described explicitly. We also present examples which demonstrate that this result cannot be extended to dimension six.

Item Type: Article
Keywords: Lattice polytope, Ehrhart polynomial, Nonsingular toric Fano, Canonical line hypothesis
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s00454-010-9275-y
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