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Licensed Unlicensed Requires Authentication Published by De Gruyter October 8, 2014

On the equality case in Ehrhart’s volume conjecture

Benjamin Nill and Andreas Paffenholz
From the journal Advances in Geometry

Abstract

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 Kähler- 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.

Published Online: 2014-10-8
Published in Print: 2014-10-1

© 2014 by Walter de Gruyter Berlin/Boston

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