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On the equality case in Ehrhart's volume conjecture
Stockholm University, Faculty of Science, Department of Mathematics.
2014 (English)In: Advances in Geometry, ISSN 1615-715X, E-ISSN 1615-7168, Vol. 14, no 4, 579-586 p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
2014. Vol. 14, no 4, 579-586 p.
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URN: urn:nbn:se:su:diva-109818DOI: 10.1515/advgeom-2014-0001ISI: 000343315000002OAI: diva2:769131


Available from: 2014-12-05 Created: 2014-12-01 Last updated: 2014-12-05Bibliographically approved

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Nill, Benjamin
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