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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 EMAIL logo 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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