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  • 1.
    Nill, Benjamin
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Paffenholz, Andreas
    On the equality case in Ehrhart's volume conjecture2014In: Advances in Geometry, ISSN 1615-715X, E-ISSN 1615-7168, Vol. 14, no 4, 579-586 p.Article in journal (Refereed)
    Abstract [en]

    Ehrhart's conjecture proposes a sharp upper bound on the volume of a convex body whose barycenter is its only interior lattice point. Recently, Berman and Berndtsson proved this conjecture for a class of rational polytopes including reflexive polytopes. In particular, they showed that the complex projective space has the maximal anticanonical degree among all toric Kahler-Einstein Fano manifolds. In this note, we prove that projective space is the only such toric manifold with maximal degree by proving the corresponding convex-geometric statement. We also discuss a generalized version of Ehrhart's conjecture involving an invariant corresponding to the so-called greatest lower bound on the Ricci curvature.

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