Discrete & Computational Geometry

, Volume 46, Issue 3, pp 488–499 | Cite as

Roots of Ehrhart Polynomials of Smooth Fano Polytopes



V. Golyshev conjectured that for any smooth polytope P with dim(P)≤5 the roots z∈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.


Lattice polytope Ehrhart polynomial Nonsingular toric Fano Canonical line hypothesis 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  2. 2.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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